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Metamath Proof Explorer

Theorem reximia

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 10-Feb-1997) (Proof shortened by Wolf Lammen, 31-Oct-2024)

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

Step	Hyp	Ref	Expression
1		ralimia.1	$⊢ x \in A \to (φ \to ψ)$
2	1	imdistani	$⊢ (x \in A \land φ) \to (x \in A \land ψ)$
3	2	reximi2	$⊢ \exists x \in A φ \to \exists x \in A ψ$