Theorem moan

Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995)

	Ref	Expression
Assertion	moan	$$⊢{\exists }^{*}x\phi \to {\exists }^{*}x\left(\psi \wedge \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		simpr	$$⊢\left(\psi \wedge \phi \right)\to \phi$$
2	1	moimi	$$⊢{\exists }^{*}x\phi \to {\exists }^{*}x\left(\psi \wedge \phi \right)$$