Theorem rmoimi

Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017)

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

Proof

Step	Hyp	Ref	Expression
1		rmoimi.1	$$⊢\phi \to \psi$$
2	1	a1i	$$⊢x\in A\to \left(\phi \to \psi \right)$$
3	2	rmoimia	$$⊢{\exists }^{*}x\in A\psi \to {\exists }^{*}x\in A\phi$$