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Metamath Proof Explorer

Theorem prodeq2sdvOLD

Description: Obsolete version of prodeq2sdv as of 1-Sep-2025. (Contributed by Scott Fenton, 4-Dec-2017) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	prodeq2sdvOLD.1	$⊢ φ \to B = C$
	Assertion	prodeq2sdvOLD	$⊢ φ \to \prod_{k \in A} B = \prod_{k \in A} C$

Proof

Step	Hyp	Ref	Expression
1		prodeq2sdvOLD.1	$⊢ φ \to B = C$
2	1	adantr	$⊢ (φ \land k \in A) \to B = C$
3	2	prodeq2dv	$⊢ φ \to \prod_{k \in A} B = \prod_{k \in A} C$