Theorem nfmo1 2587

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		dfmo 2570	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfexa2 2215	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
3	1, 2	nfxfr 1886	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

This proof depends on syntax axioms:   → wi 4  ∀wal 1568  ∃wex 1812  Ⅎwnf 1816  ∃*wmo 2567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-10 2179  ax-11 2195

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-nf 1817  df-mo 2569

This theorem is used by:  mo3  2594  nfeu1  2619  moanmo  2652  moexexlem  2656  mopick2  2667  2mo  2678  2eu3  2683  nfrmo1  3398  mob  3682  morex  3684  wl-mo3t  38290  permaxrep  45775