Theorem prodeq2ad

Description: Equality deduction for product. (Contributed by Glauco Siliprandi, 5-Apr-2020)

	Ref	Expression
Hypothesis	prodeq2ad.1	|- ( ph -> B = C )
Assertion	prodeq2ad	|- ( ph -> prod_ k e. A B = prod_ k e. A C )

Proof

Step	Hyp	Ref	Expression
1		prodeq2ad.1	|- ( ph -> B = C )
2	1	ralrimivw	|- ( ph -> A. k e. A B = C )
3	2	prodeq2d	|- ( ph -> prod_ k e. A B = prod_ k e. A C )