Theorem moani

Description: "At most one" is still true when a conjunct is added, inference form. (Contributed by NM, 9-Mar-1995)

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

Proof

Step	Hyp	Ref	Expression
1		moani.1	$$⊢{\exists }^{*}x\phi$$
2		moan	$$⊢{\exists }^{*}x\phi \to {\exists }^{*}x\left(\psi \wedge \phi \right)$$
3	1 2	ax-mp	$$⊢{\exists }^{*}x\left(\psi \wedge \phi \right)$$