This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem prodeq2dv

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

		Ref	Expression
	Hypothesis	prodeq2dv.1	$⊢ (φ \land k \in A) \to B = C$
	Assertion	prodeq2dv	$⊢ φ \to \prod_{k \in A} B = \prod_{k \in A} C$

Step	Hyp	Ref	Expression
1		prodeq2dv.1	$⊢ (φ \land k \in A) \to B = C$
2	1	ralrimiva	$⊢ φ \to \forall k \in A B = C$
3	2	prodeq2d	$⊢ φ \to \prod_{k \in A} B = \prod_{k \in A} C$