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 e. _V
Assertion	epeli	|- ( A _E B <-> A e. B )

Proof

Step	Hyp	Ref	Expression
1		epeli.1	|- B e. _V
2		epelg	|- ( B e. _V -> ( A _E B <-> A e. B ) )
3	1 2	ax-mp	|- ( A _E B <-> A e. B )