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Metamath Proof Explorer

Theorem ralimia

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 19-Jul-1996)

		Ref	Expression
	Hypothesis	ralimia.1	$⊢ x \in A \to (φ \to ψ)$
	Assertion	ralimia	$⊢ \forall x \in A φ \to \forall x \in A ψ$

Step	Hyp	Ref	Expression
1		ralimia.1	$⊢ x \in A \to (φ \to ψ)$
2	1	a2i	$⊢ (x \in A \to φ) \to (x \in A \to ψ)$
3	2	ralimi2	$⊢ \forall x \in A φ \to \forall x \in A ψ$