Theorem nfmo1 2584

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 2567	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfexa2 2211	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
3	1, 2	nfxfr 1873	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1558  ∃wex 1799  Ⅎwnf 1803  ∃*wmo 2564

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-10 2175  ax-11 2191

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1800  df-nf 1804  df-mo 2566

This theorem is referenced by:  mo3  2591  nfeu1  2616  moanmo  2649  moexexlem  2653  mopick2  2664  2mo  2675  2eu3  2680  nfrmo1  3394  mob  3680  morex  3682  wl-mo3t  38079  permaxrep  45582