# Using the laws of logic prove that $[\neg q \land (p \rightarrow q)] \rightarrow \neg p$ is a tautology

Could someone please tell me if I am correct and if I am not, tell me where I went wrong?

Using the laws of logic prove that $[\neg q \land (p \rightarrow q)] \rightarrow \neg p$ is a tautology.

First I used the Implication law $(p \rightarrow q) \equiv (\neg p \vee q)$ to show that $$[\neg q \land (p \rightarrow q)] \equiv [\neg q \land (\neg p \vee q)]$$

Then I "factored" (?) the $\neg$ out and had $$\neg [q \vee (p \land \neg q)]$$