I need to prove that $(\neg p \wedge (p \vee q)) \rightarrow q $ is a tautology using Laws of Logic (not truth tables).
This is what I tried:
$\equiv (( \neg p \wedge p) \vee (\neg p \wedge q)) \rightarrow q \\ \equiv (F \vee (\neg p \wedge q)) \rightarrow q \\ \equiv (\neg p \wedge q) \rightarrow q \\ \equiv (F) \rightarrow q \\ \equiv T $
Is this logically correct? The laws I used in order were: Distributive, then negation, and identity. My only issue is with the last step where I know the truth values of $(\neg p \wedge q)$ are all $F$ but I dont know what law it uses.
Please Help!