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Metamath Proof Explorer

Theorem prodeq1d

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

		Ref	Expression
	Hypothesis	prodeq1d.1	$⊢ φ \to A = B$
	Assertion	prodeq1d	$⊢ φ \to \prod_{k \in A} C = \prod_{k \in B} C$

Step	Hyp	Ref	Expression
1		prodeq1d.1	$⊢ φ \to A = B$
2		prodeq1	$⊢ A = B \to \prod_{k \in A} C = \prod_{k \in B} C$
3	1 2	syl	$⊢ φ \to \prod_{k \in A} C = \prod_{k \in B} C$