Theorem nfmo1 2585

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 2568	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfexa2 2214	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
3	1, 2	nfxfr 1885	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

This proof depends on syntax axioms:   → wi 4  ∀wal 1567  ∃wex 1811  Ⅎwnf 1815  ∃*wmo 2565

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-10 2179  ax-11 2196

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-nf 1816  df-mo 2567

This theorem is used by:  mo3  2592  nfeu1  2617  moanmo  2650  moexexlem  2654  mopick2  2665  2mo  2676  2eu3  2681  nfrmo1  3395  mob  3677  morex  3679  wl-mo3t  38648  permaxrep  46135