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Metamath Proof Explorer

Theorem ralimdvvOLD

Description: Obsolete version of ralimdvv as of 18-Nov-2025. (Contributed by Scott Fenton, 2-Mar-2025) (New usage is discouraged.) (Proof modification is discouraged.)

		Ref	Expression
	Hypothesis	ralimdvvOLD.1	$⊢ φ \to (ψ \to χ)$
	Assertion	ralimdvvOLD	$⊢ φ \to (\forall x \in A \forall y \in B ψ \to \forall x \in A \forall y \in B χ)$

Proof

Step	Hyp	Ref	Expression
1		ralimdvvOLD.1	$⊢ φ \to (ψ \to χ)$
2	1	adantr	$⊢ (φ \land (x \in A \land y \in B)) \to (ψ \to χ)$
3	2	ralimdvva	$⊢ φ \to (\forall x \in A \forall y \in B ψ \to \forall x \in A \forall y \in B χ)$