Theorem elintab

Description: Membership in the intersection of a class abstraction. (Contributed by NM, 30-Aug-1993)

	Ref	Expression
Hypothesis	elintab.ex	|- A e. _V
Assertion	elintab	|- ( A e. |^| { x | ph } <-> A. x ( ph -> A e. x ) )

Proof

Step	Hyp	Ref	Expression
1		elintab.ex	|- A e. _V
2		elintabg	|- ( A e. _V -> ( A e. |^| { x | ph } <-> A. x ( ph -> A e. x ) ) )
3	1 2	ax-mp	|- ( A e. |^| { x | ph } <-> A. x ( ph -> A e. x ) )