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Metamath Proof Explorer

Theorem 2alimi

Description: Inference doubly quantifying both antecedent and consequent. (Contributed by NM, 3-Feb-2005)

		Ref	Expression
	Hypothesis	alimi.1	$⊢ φ \to ψ$
	Assertion	2alimi	$⊢ \forall x \forall y φ \to \forall x \forall y ψ$

Step	Hyp	Ref	Expression
1		alimi.1	$⊢ φ \to ψ$
2	1	alimi	$⊢ \forall y φ \to \forall y ψ$
3	2	alimi	$⊢ \forall x \forall y φ \to \forall x \forall y ψ$