Theorem nfmo1 2547

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.)

Assertion

Ref	Expression
nfmo1	⊢ Ⅎ𝑥∃*𝑥𝜑

Proof of Theorem nfmo1

Dummy variable 𝑦 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mo 2530	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfa1 2141	. . 3 ⊢ Ⅎ𝑥∀𝑥(𝜑 → 𝑥 = 𝑦)
3	2	nfex 2313	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
4	1, 3	nfxfr 1848	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1532  ∃wex 1774  Ⅎwnf 1778  ∃*wmo 2528

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-11 2147  ax-12 2167

This theorem depends on definitions:  df-bi 206  df-or 847  df-ex 1775  df-nf 1779  df-mo 2530

This theorem is referenced by:  mo3  2554  nfeu1ALT  2579  moanmo  2614  moexexlem  2618  mopick2  2629  2mo  2640  2eu3  2645  nfrmo1  3403  mob  3711  morex  3713  wl-mo3t  37038

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