Theorem elintdv

Description: Membership in class intersection. (Contributed by Glauco Siliprandi, 3-Jan-2021)

	Ref	Expression
Hypotheses	elintdv.1	|- ( ph -> A e. V )
	elintdv.2	|- ( ( ph /\ x e. B ) -> A e. x )
Assertion	elintdv	|- ( ph -> A e. |^| B )

Proof

Step	Hyp	Ref	Expression
1		elintdv.1	|- ( ph -> A e. V )
2		elintdv.2	|- ( ( ph /\ x e. B ) -> A e. x )
3		nfv	|- F/ x ph
4	3 1 2	elintd	|- ( ph -> A e. |^| B )