I have to prove a problem statement with logical equivalences but I seem to keep getting stuck. Here is the problem: $$ [(q \to p) \land \lnot p] \to (p \land q) \equiv p \lor q $$ Here is the work I have so far: $$\equiv \lnot [(\lnot q \lor p) \land \lnot p] \lor (p \land q) $$ $$\equiv [( q \land \lnot p) \lor p] \lor (p \land q) $$ $$\equiv [( p \lor q) \land (p \lor \lnot p)] \lor (p \land q) $$ $$\equiv [( p \lor q) \land T] \lor (p \land q) $$ $$\equiv ( p \lor q) \lor (p \land q) $$
Any hints or pointing out mistakes I made so far would be great