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Metamath Proof Explorer

Theorem prodeq2i

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

		Ref	Expression
	Hypothesis	prodeq2i.1	$⊢ k \in A \to B = C$
	Assertion	prodeq2i	$⊢ \prod_{k \in A} B = \prod_{k \in A} C$

Step	Hyp	Ref	Expression
1		prodeq2i.1	$⊢ k \in A \to B = C$
2		prodeq2	$⊢ \forall k \in A B = C \to \prod_{k \in A} B = \prod_{k \in A} C$
3	2 1	mprg	$⊢ \prod_{k \in A} B = \prod_{k \in A} C$