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 B V
Assertion epeli A E B A B


Step Hyp Ref Expression
1 epeli.1 B V
2 epelg B V A E B A B
3 1 2 ax-mp A E B A B