`\implies` requires the AMSsymbol extension which is not enabled. But many symbols have a reasonable replacement, or you could directly put a Unicode symbol.
The following shows a list of unsupported AMSsymbol symbols, and their replacements,
\digamma = ϝ or ϝ
\varkappa = ϰ or ϰ
\varGamma = \mathit\Gamma
\varDelta = \mathit\Delta
\varTheta = \mathit\Theta
\varLambda = \mathit\Lambda
\varXi = \mathit\Xi
\varPi = \mathit\Pi
\varSigma = \mathit\Sigma
\varUpsilon = \mathit\Upsilon
\varPhi = \mathit\Phi
\varPsi = \mathit\Psi
\varOmega = \mathit\Omega
\beth = ℶ or ℶ
\gimel = ℷ or ℷ
\daleth = ℸ or ℸ
\backprime = ‵ or ‵
\hslash = \unicode[MathJax_AMS]{x210f}
\varnothing = \unicode[MathJax_AMS]{x2205}
\blacktriangle = ▲ or ▲
\triangledown = \unicode[MathJax_AMS]{x25bd}
\blacktriangledown = ▼ or ▼
\square = □ or □
\Box = □ or □
\blacksquare = ■ or ■
\lozenge = ◊ or ◊
\Diamond = ◊ or ◊
\blacklozenge = ⧫ or ⧫
\circledS = Ⓢ or Ⓢ
\bigstar = ★ or ★ or {\Large\star}
\sphericalangle = ∢ or ∢
\measuredangle = ∡ or ∡
\nexists = ∄ or ∄
\complement = ∁ or ∁
\mho = ℧ or ℧
\eth = ð or ð
\Finv = Ⅎ or Ⅎ
\diagup = ╱ or ╱
\Game = ⅁ or ⅁
\diagdown = ╲ or ╲
\Bbbk = \mathbb{k}
\yen = ¥ or ¥
\circledR = ® or ®
\checkmark = ✓ or ✓
\maltese = ✠ or ✠
\dotplus = ∔ or ∔ or \mathop{\dot+}
\ltimes = ⋉ or ⋉
\smallsetminus = \mathrel{\unicode[MathJax_AMS]{x2216}}
\rtimes = ⋊ or ⋊
\Cap = ⋒ or ⋒
\doublecap = ⋒ or ⋒
\leftthreetimes = ⋋ or ⋋
\Cup = ⋓ or ⋓
\doublecup = ⋓ or ⋓
\rightthreetimes = ⋌ or ⋌
\barwedge = ⊼ or ⊼ or \bar\wedge
\curlywedge = ⋏ or ⋏
\veebar = ⊻ or ⊻
\curlyvee = ⋎ or ⋎
\doublebarwedge = ⩞ or ⩞ or \bar{\bar\wedge}
\boxminus = ⊟ or ⊟
\circleddash = ⊝ or ⊝
\boxtimes = ⊠ or ⊠
\circledast = ⊛ or ⊛
\boxdot = ⊡ or ⊡
\circledcirc = ⊚ or ⊚
\boxplus = ⊞ or ⊞
\centerdot = \cdot or ⋅
\divideontimes = ⋇ or ⋇
\intercal = ⊺ or ⊺
\leqq = ≦ or ≦
\geqq = ≧ or ≧
\leqslant = ⩽ or ⩽
\geqslant = ⩾ or ⩾
\eqslantless = ⪕ or ⪕
\eqslantgtr = ⪖ or ⪖
\lesssim = ≲ or ≲
\gtrsim = ≳ or ≳
\lessapprox = ⪅ or ⪅
\gtrapprox = ⪆ or ⪆
\approxeq = ≊ or ≊
\lessdot = ⋖ or ⋖
\gtrdot = ⋗ or ⋗
\lll = ⋘ or ⋘
\llless = ⋘ or ⋘
\ggg = ⋙ or ⋙
\gggtr = ⋙ or ⋙
\lessgtr = ≶ or ≶
\gtrless = ≷ or ≷
\lesseqgtr = ⋚ or ⋚
\gtreqless = ⋛ or ⋛
\lesseqqgtr = ⪋ or ⪋
\gtreqqless = ⪌ or ⪌
\doteqdot = ≑ or ≑
\Doteq = ≑ or ≑
\eqcirc = ≖ or ≖
\risingdotseq = ≓ or ≓
\circeq = ≗ or ≗
\fallingdotseq = ≒ or ≒
\triangleq = ≜ or ≜
\backsim = ∽ or ∽
\thicksim = \mathrel{\unicode[MathJax_AMS]{x223c}}
\backsimeq = ⋍ or ⋍
\thickapprox = \mathrel{\unicode[MathJax_AMS]{x2248}}
\subseteqq = ⫅ or ⫅
\supseteqq = ⫆ or ⫆
\Subset = ⋐ or ⋐
\Supset = ⋑ or ⋑
\sqsubset = ⊏ or ⊏
\sqsupset = ⊐ or ⊐
\preccurlyeq = ≼ or ≼
\succcurlyeq = ≽ or ≽
\curlyeqprec = ⋞ or ⋞
\curlyeqsucc = ⋟ or ⋟
\precsim = ≾ or ≾
\succsim = ≿ or ≿
\precapprox = ⪷ or ⪷
\succapprox = ⪸ or ⪸
\vartriangleleft = ⊲ or ⊲
\lhd = ⊲ or ⊲
\vartriangleright = ⊳ or ⊳
\rhd = ⊳ or ⊳
\trianglelefteq = ⊴ or ⊴
\unlhd = ⊴ or ⊴
\trianglerighteq = ⊵ or ⊵
\unrhd = ⊵ or ⊵
\vDash = ⊨ or ⊨
\Vdash = ⊩ or ⊩
\Vvdash = ⊪ or ⊪
\smallsmile = \mathrel{\unicode[MathJax_AMS]{x2323}}
\shortmid = \mathrel{\unicode[MathJax_AMS]{x2223}}
\smallfrown = \mathrel{\unicode[MathJax_AMS]{x2322}}
\shortparallel = \mathrel{\unicode[MathJax_AMS]{x2225}}
\bumpeq = ≏ or ≏
\between = ≬ or ≬
\Bumpeq = ≎ or ≎
\pitchfork = ⋔ or ⋔
\varpropto = \mathrel{\unicode[MathJax_AMS]{x221d}}
\backepsilon = ∍ or ∍
\blacktriangleleft = ◀ or ◀
\blacktriangleright = ▶ or ▶
\therefore = ∴ or ∴
\because = ∵ or ∵
\eqsim = ≂ or ≂
\vartriangle = \mathrel{\unicode[MathJax_AMS]{x25b3}}
\Join = ⋈ or ⋈
\nless = ≮ or ≮ or \not<
\ngtr = ≯ or ≯ or \not>
\nleq = ≰ or ≰ or \not\le
\ngeq = ≱ or ≱ or \not\ge
\nleqslant = \mathrel or \not⩽
\ngeqslant = \mathrel or \not⩾
\nleqq = \mathrel or \not≦
\ngeqq = \mathrel or \not≧
\lneq = ⪇ or ⪇
\gneq = ⪈ or ⪈
\lneqq = ≨ or ≨
\gneqq = ≩ or ≩
\lvertneqq = \mathrel
\gvertneqq = \mathrel
\lnsim = ⋦ or ⋦
\gnsim = ⋧ or ⋧
\lnapprox = ⪉ or ⪉
\gnapprox = ⪊ or ⪊
\nprec = ⊀ or ⊀ or \not\prec
\nsucc = ⊁ or ⊁ or \not\succ
\npreceq = ⋠ or ⋠ or \not\preceq
\nsucceq = ⋡ or ⋡ or \not\succeq
\precneqq = ⪵ or ⪵
\succneqq = ⪶ or ⪶
\precnsim = ⋨ or ⋨
\succnsim = ⋩ or ⋩
\precnapprox = ⪹ or ⪹
\succnapprox = ⪺ or ⪺
\nsim = ≁ or ≁
\ncong = ≆ or ≆ or \not\cong
\nshortmid = \mathrel
\nshortparallel = \mathrel
\nmid = ∤ or ∤
\nparallel = ∦ or ∦
\nvdash = ⊬ or ⊬
\nvDash = ⊭ or ⊭
\nVdash = ⊮ or ⊮
\nVDash = ⊯ or ⊯
\ntriangleleft = ⋪ or ⋪
\ntriangleright = ⋫ or ⋫
\ntrianglelefteq = ⋬ or ⋬
\ntrianglerighteq = ⋭ or ⋭
\nsubseteq = ⊈ or ⊈ or \not\subseteq
\nsupseteq = ⊉ or ⊉ or \not\supseteq
\nsubseteqq = \mathrel or \not⫅
\nsupseteqq = \mathrel or \not⫆
\subsetneq = ⊊ or ⊊
\supsetneq = ⊋ or ⊋
\varsubsetneq = \mathrel
\varsupsetneq = \mathrel
\subsetneqq = ⫋ or ⫋
\supsetneqq = ⫌ or ⫌
\varsubsetneqq = \mathrel
\varsupsetneqq = \mathrel
\leftleftarrows = ⇇ or ⇇
\rightrightarrows = ⇉ or ⇉
\leftrightarrows = ⇆ or ⇆
\rightleftarrows = ⇄ or ⇄
\Lleftarrow = ⇚ or ⇚
\Rrightarrow = ⇛ or ⇛
\twoheadleftarrow = ↞ or ↞
\twoheadrightarrow = ↠ or ↠
\leftarrowtail = ↢ or ↢
\rightarrowtail = ↣ or ↣
\looparrowleft = ↫ or ↫
\looparrowright = ↬ or ↬
\leftrightharpoons = ⇋ or ⇋
\rightleftharpoons = ⇌ or ⇌
\curvearrowleft = ↶ or ↶
\curvearrowright = ↷ or ↷
\circlearrowleft = ↺ or ↺
\circlearrowright = ↻ or ↻
\Lsh = ↰ or ↰
\Rsh = ↱ or ↱
\upuparrows = ⇈ or ⇈
\downdownarrows = ⇊ or ⇊
\upharpoonleft = ↿ or ↿
\upharpoonright = ↾ or ↾
\downharpoonleft = ⇃ or ⇃
\restriction = ↾ or ↾
\multimap = ⊸ or ⊸
\downharpoonright = ⇂ or ⇂
\leftrightsquigarrow = ↭ or ↭
\rightsquigarrow = ⇝ or ⇝
\leadsto = ⇝ or ⇝
\dashrightarrow = ⇢ or ⇢
\dashleftarrow = ⇠ or ⇠
\nleftarrow = ↚ or Ûa;
\nrightarrow = ↛ or Ûb;
\nLeftarrow = ⇍ or cd;
\nRightarrow = ⇏ or cf;
\nleftrightarrow = ↮ or ae;
\nLeftrightarrow = ⇎ or ce;
\ulcorner = ┌ or ┌
\urcorner = ┐ or ┐
\llcorner = └ or └
\lrcorner = ┘ or ┘
\implies = \;\Longrightarrow\;
\impliedby = \;\Longleftarrow\;