Theorem ixpeq1d

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

	Ref	Expression
Hypothesis	ixpeq1d.1	|- ( ph -> A = B )
Assertion	ixpeq1d	|- ( ph -> X_ x e. A C = X_ x e. B C )

Proof

Step	Hyp	Ref	Expression
1		ixpeq1d.1	|- ( ph -> A = B )
2		ixpeq1	|- ( A = B -> X_ x e. A C = X_ x e. B C )
3	1 2	syl	|- ( ph -> X_ x e. A C = X_ x e. B C )