Theorem prodeq1d

Description: Equality deduction for product. (Contributed by Scott Fenton, 4-Dec-2017)

	Ref	Expression
Hypothesis	prodeq1d.1	|- ( ph -> A = B )
Assertion	prodeq1d	|- ( ph -> prod_ k e. A C = prod_ k e. B C )

Proof

Step	Hyp	Ref	Expression
1		prodeq1d.1	|- ( ph -> A = B )
2		prodeq1	|- ( A = B -> prod_ k e. A C = prod_ k e. B C )
3	1 2	syl	|- ( ph -> prod_ k e. A C = prod_ k e. B C )