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Metamath Proof Explorer

Theorem reximi

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 18-Oct-1996)

		Ref	Expression
	Hypothesis	ralimi.1	$⊢ φ \to ψ$
	Assertion	reximi	$⊢ \exists x \in A φ \to \exists x \in A ψ$

Step	Hyp	Ref	Expression
1		ralimi.1	$⊢ φ \to ψ$
2	1	a1i	$⊢ x \in A \to (φ \to ψ)$
3	2	reximia	$⊢ \exists x \in A φ \to \exists x \in A ψ$