Theorem mormo

Description: Unrestricted "at most one" implies restricted "at most one". (Contributed by NM, 16-Jun-2017)

	Ref	Expression
Assertion	mormo	$$⊢{\exists }^{*}x\phi \to {\exists }^{*}x\in A\phi$$

Proof

Step	Hyp	Ref	Expression
1		moan	$$⊢{\exists }^{*}x\phi \to {\exists }^{*}x\left(x\in A\wedge \phi \right)$$
2		df-rmo	$$⊢{\exists }^{*}x\in A\phi \leftrightarrow {\exists }^{*}x\left(x\in A\wedge \phi \right)$$
3	1 2	sylibr	$$⊢{\exists }^{*}x\phi \to {\exists }^{*}x\in A\phi$$