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Metamath Proof Explorer

Theorem moimi

Description: The at-most-one quantifier reverses implication. (Contributed by NM, 15-Feb-2006)

		Ref	Expression
	Hypothesis	moimi.1	$⊢ φ \to ψ$
	Assertion	moimi	$⊢ \exists^{} x ψ \to \exists^{} x φ$

Step	Hyp	Ref	Expression
1		moimi.1	$⊢ φ \to ψ$
2		moim	$⊢ \forall x (φ \to ψ) \to (\exists^{} x ψ \to \exists^{} x φ)$
3	2 1	mpg	$⊢ \exists^{} x ψ \to \exists^{} x φ$