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Metamath Proof Explorer

Theorem nfmo

Description: Bound-variable hypothesis builder for the at-most-one quantifier. Note that x and y need not be disjoint. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfmov when possible. (Contributed by NM, 9-Mar-1995) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	nfmo.1	$⊢ Ⅎ x φ$
	Assertion	nfmo	$⊢ Ⅎ x \exists^{*} y φ$

Proof

Step	Hyp	Ref	Expression
1		nfmo.1	$⊢ Ⅎ x φ$
2		nftru	$⊢ Ⅎ y ⊤$
3	1	a1i	$⊢ ⊤ \to Ⅎ x φ$
4	2 3	nfmod	$⊢ ⊤ \to Ⅎ x \exists^{*} y φ$
5	4	mptru	$⊢ Ⅎ x \exists^{*} y φ$