The statement I am trying to simplify is: $\lnot(p\lor\lnot q)\to(p\to(p\land\lnot p))$
First thing I did was use the Material Implication Law resulting:
$\lnot\lnot(p\lor\lnot q)\lor(\lnot p\lor(p\land\lnot p))$
$(p\lor\lnot q)\lor(\lnot p\lor(p\land\lnot p))$
Then I distributed the right side resulting in:
$(p\lor\lnot q)\lor((\lnot p\lor p)\land(\lnot p\lor\lnot p))$
And since $(\lnot p\lor\lnot p)=\lnot p$:
$(p\lor\lnot q)\lor((\lnot p\lor p)\land\lnot p)$
And since $\lnot p\lor p=\top$:
$(p\lor\lnot q)\lor(\top\land\lnot p)$
Up to there is where I feel stucked and I am not sure if I did it correctly and would like appreciate some feedback if its correct or wrong and what can I do to solve it better. Thanks in advance!