There was a post on m.se a few days ago, I want to say Thursday or Friday night (SEpt 17th or 18th 2015) where a user was asking for help showing some propositional logic result without using truth tables. It was pretty similar to this question but the proposition in question was a little more complex with a bunch of nested implications. Something like $((p\vee q)\rightarrow r)\wedge((\neg p\vee s)\rightarrow t)\rightarrow q\wedge s$. That's not right, clearly, but it was something like that. And then the user lists that he's allowed to use the identities $p\vee T=T$, $p\wedge F=F$, etc.
I've been searching for the post with no success, and I presume it's been deleted. Is it easy for someone with high privileges to find such things and share them?