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Metamath Proof Explorer

Theorem alimi

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 5-Jan-1993)

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

Step	Hyp	Ref	Expression
1		alimi.1	$⊢ φ \to ψ$
2		alim	$⊢ \forall x (φ \to ψ) \to (\forall x φ \to \forall x ψ)$
3	2 1	mpg	$⊢ \forall x φ \to \forall x ψ$