Theorem prodeq2i

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

	Ref	Expression
Hypothesis	prodeq2i.1	|- ( k e. A -> B = C )
Assertion	prodeq2i	|- prod_ k e. A B = prod_ k e. A C

Proof

Step	Hyp	Ref	Expression
1		prodeq2i.1	|- ( k e. A -> B = C )
2		prodeq2	|- ( A. k e. A B = C -> prod_ k e. A B = prod_ k e. A C )
3	2 1	mprg	|- prod_ k e. A B = prod_ k e. A C