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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 ∃* 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		df-mo	⊢ ( ∃* 𝑥 𝜑 ↔ ∃ 𝑦 ∀ 𝑥 ( 𝜑 → 𝑥 = 𝑦 ) )
2		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 ( 𝜑 → 𝑥 = 𝑦 )
3	2	nfex	⊢ Ⅎ 𝑥 ∃ 𝑦 ∀ 𝑥 ( 𝜑 → 𝑥 = 𝑦 )
4	1 3	nfxfr	⊢ Ⅎ 𝑥 ∃* 𝑥 𝜑