Theorem nfmo1 2561

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 2544	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfexa2 2188	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
3	1, 2	nfxfr 1860	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1545  ∃wex 1786  Ⅎwnf 1790  ∃*wmo 2541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-10 2152  ax-11 2168

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-nf 1791  df-mo 2543

This theorem is referenced by:  mo3  2568  nfeu1  2593  moanmo  2626  moexexlem  2630  mopick2  2641  2mo  2652  2eu3  2657  nfrmo1  3371  mob  3658  morex  3660  wl-mo3t  37947  permaxrep  45450