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 B B 𝒫 C A C


Step Hyp Ref Expression
1 elpwi B 𝒫 C B C
2 1 sseld B 𝒫 C A B A C
3 2 impcom A B B 𝒫 C A C