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Metamath Proof Explorer

Theorem ralimiaa

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 4-Aug-2007)

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

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