Theorem clel3

Description: An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993)

	Ref	Expression
Hypothesis	clel3.1	|- B e. _V
Assertion	clel3	|- ( A e. B <-> E. x ( x = B /\ A e. x ) )

Proof

Step	Hyp	Ref	Expression
1		clel3.1	|- B e. _V
2		clel3g	|- ( B e. _V -> ( A e. B <-> E. x ( x = B /\ A e. x ) ) )
3	1 2	ax-mp	|- ( A e. B <-> E. x ( x = B /\ A e. x ) )