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Metamath Proof Explorer

Theorem eximi

Description: Inference adding existential quantifier to antecedent and consequent. (Contributed by NM, 10-Jan-1993)

		Ref	Expression
	Hypothesis	eximi.1	$⊢ φ \to ψ$
	Assertion	eximi	$⊢ \exists x φ \to \exists x ψ$

Step	Hyp	Ref	Expression
1		eximi.1	$⊢ φ \to ψ$
2		exim	$⊢ \forall x (φ \to ψ) \to (\exists x φ \to \exists x ψ)$
3	2 1	mpg	$⊢ \exists x φ \to \exists x ψ$