Theorem nfmo1 2560

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 2543	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfa1 2152	. . 3 ⊢ Ⅎ𝑥∀𝑥(𝜑 → 𝑥 = 𝑦)
3	2	nfex 2328	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
4	1, 3	nfxfr 1851	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1535  ∃wex 1777  Ⅎwnf 1781  ∃*wmo 2541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2158  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-or 847  df-ex 1778  df-nf 1782  df-mo 2543

This theorem is referenced by:  mo3  2567  nfeu1ALT  2592  moanmo  2625  moexexlem  2629  mopick2  2640  2mo  2651  2eu3  2657  nfrmo1  3419  mob  3739  morex  3741  wl-mo3t  37530