Metamath Proof Explorer

Theorem iscnrm3lem6

Description: Lemma for iscnrm3lem7 . (Contributed by Zhi Wang, 5-Sep-2024)

		Ref	Expression
	Hypothesis	iscnrm3lem6.1	$⊢ (φ \land (x \in V \land y \in W) \land ψ) \to χ$
	Assertion	iscnrm3lem6	$⊢ φ \to (\exists x \in V \exists y \in W ψ \to χ)$

Step	Hyp	Ref	Expression
1		iscnrm3lem6.1	$⊢ (φ \land (x \in V \land y \in W) \land ψ) \to χ$
2	1	3exp	$⊢ φ \to ((x \in V \land y \in W) \to (ψ \to χ))$
3	2	rexlimdvv	$⊢ φ \to (\exists x \in V \exists y \in W ψ \to χ)$