Theorem clel2

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

	Ref	Expression
Hypothesis	clel2.1	|- A e. _V
Assertion	clel2	|- ( A e. B <-> A. x ( x = A -> x e. B ) )

Proof

Step	Hyp	Ref	Expression
1		clel2.1	|- A e. _V
2		clel2g	|- ( A e. _V -> ( A e. B <-> A. x ( x = A -> x e. B ) ) )
3	1 2	ax-mp	|- ( A e. B <-> A. x ( x = A -> x e. B ) )