Metamath Proof Explorer

Theorem elelpwi

Description: If A belongs to a part of C , then A belongs to C . (Contributed by FL, 3-Aug-2009)

Ref Expression
Assertion elelpwi 
|- ( ( A e. B /\ B e. ~P C ) -> A e. C )

Proof

Step Hyp Ref Expression
1 elpwi 
 |-  ( B e. ~P C -> B C_ C )
2 1 sseld 
 |-  ( B e. ~P C -> ( A e. B -> A e. C ) )
3 2 impcom 
 |-  ( ( A e. B /\ B e. ~P C ) -> A e. C )