# How to prove P = NP if problem Π ϵ NP-complete and Problem complement Πc ϵ NP?

How to prove if P = NP if problem Π ϵ NP-complete and Problem complement Πc ϵ NP? OR P = NP if NPC intersects with Co-NPC

Proving $$NP=co-NP$$ doesn't necessarily mean that $$P=NP$$. Although, the other way around is correct: Assume $$P=NP$$, then $$co-NP=co-P=P=NP$$.
You won't find anything useful with our current knowledge. However, a change to $$\Pi^c\in \mbox{P}$$ will get you $$\mbox{P}=\mbox{NP}$$.