Theorem ixpeq2dv

Description: Equality theorem for infinite Cartesian product. (Contributed by Mario Carneiro, 11-Jun-2016)

	Ref	Expression
Hypothesis	ixpeq2dv.1	|- ( ph -> B = C )
Assertion	ixpeq2dv	|- ( ph -> X_ x e. A B = X_ x e. A C )

Proof

Step	Hyp	Ref	Expression
1		ixpeq2dv.1	|- ( ph -> B = C )
2	1	adantr	|- ( ( ph /\ x e. A ) -> B = C )
3	2	ixpeq2dva	|- ( ph -> X_ x e. A B = X_ x e. A C )