Theorem moimi

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

	Ref	Expression
Hypothesis	moimi.1	$$⊢\phi \to \psi$$
Assertion	moimi	$$⊢{\exists }^{*}x\psi \to {\exists }^{*}x\phi$$

Proof

Step	Hyp	Ref	Expression
1		moimi.1	$$⊢\phi \to \psi$$
2		moim	$$⊢\forall x\left(\phi \to \psi \right)\to \left({\exists }^{*}x\psi \to {\exists }^{*}x\phi \right)$$
3	2 1	mpg	$$⊢{\exists }^{*}x\psi \to {\exists }^{*}x\phi$$