Theorem moimdv

Description: The at-most-one quantifier reverses implication, deduction form. (Contributed by Thierry Arnoux, 25-Feb-2017)

	Ref	Expression
Hypothesis	moimdv.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	moimdv	$$⊢\phi \to \left({\exists }^{*}x\chi \to {\exists }^{*}x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		moimdv.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	alrimiv	$$⊢\phi \to \forall x\left(\psi \to \chi \right)$$
3		moim	$$⊢\forall x\left(\psi \to \chi \right)\to \left({\exists }^{*}x\chi \to {\exists }^{*}x\psi \right)$$
4	2 3	syl	$$⊢\phi \to \left({\exists }^{*}x\chi \to {\exists }^{*}x\psi \right)$$