Theorem nfmo1

Description: Bound-variable hypothesis builder for the at-most-one quantifier. (Contributed by NM, 8-Mar-1995) (Revised by Mario Carneiro, 7-Oct-2016) Adapt to new definition. (Revised by BJ, 1-Oct-2022)

	Ref	Expression
Assertion	nfmo1	$$⊢Ⅎx{\exists }^{*}x\phi$$

Proof

Step	Hyp	Ref	Expression
1		df-mo	$$⊢{\exists }^{*}x\phi \leftrightarrow \exists y\forall x\left(\phi \to x=y\right)$$
2		nfa1	$$⊢Ⅎx\forall x\left(\phi \to x=y\right)$$
3	2	nfex	$$⊢Ⅎx\exists y\forall x\left(\phi \to x=y\right)$$
4	1 3	nfxfr	$$⊢Ⅎx{\exists }^{*}x\phi$$