Metamath Proof Explorer


Theorem epeli

Description: The membership relation and the membership predicate agree when the "containing" class is a set. Inference associated with epelg . (Contributed by Scott Fenton, 11-Apr-2012)

Ref Expression
Hypothesis epeli.1 BV
Assertion epeli AEBAB

Proof

Step Hyp Ref Expression
1 epeli.1 BV
2 epelg BVAEBAB
3 1 2 ax-mp AEBAB