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Metamath Proof Explorer

Theorem nfmov

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo for a version without disjoint variable conditions but requiring ax-13 . (Contributed by NM, 9-Mar-1995) (Revised by Wolf Lammen, 2-Oct-2023)

		Ref	Expression
	Hypothesis	nfmov.1	⊢ Ⅎ 𝑥 𝜑
	Assertion	nfmov	⊢ Ⅎ 𝑥 ∃* 𝑦 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfmov.1	⊢ Ⅎ 𝑥 𝜑
2		nftru	⊢ Ⅎ 𝑦 ⊤
3	1	a1i	⊢ ( ⊤ → Ⅎ 𝑥 𝜑 )
4	2 3	nfmodv	⊢ ( ⊤ → Ⅎ 𝑥 ∃* 𝑦 𝜑 )
5	4	mptru	⊢ Ⅎ 𝑥 ∃* 𝑦 𝜑