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Metamath Proof Explorer

Theorem prodeq2ad

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

		Ref	Expression
	Hypothesis	prodeq2ad.1	$⊢ φ \to B = C$
	Assertion	prodeq2ad	$⊢ φ \to \prod_{k \in A} B = \prod_{k \in A} C$

Step	Hyp	Ref	Expression
1		prodeq2ad.1	$⊢ φ \to B = C$
2	1	ralrimivw	$⊢ φ \to \forall k \in A B = C$
3	2	prodeq2d	$⊢ φ \to \prod_{k \in A} B = \prod_{k \in A} C$