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Metamath Proof Explorer

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	$⊢ Ⅎ x \exists^{*} x φ$

Proof

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