Theorem nfmo1 2552

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 2535	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfa1 2154	. . 3 ⊢ Ⅎ𝑥∀𝑥(𝜑 → 𝑥 = 𝑦)
3	2	nfex 2325	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
4	1, 3	nfxfr 1854	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1539  ∃wex 1780  Ⅎwnf 1784  ∃*wmo 2533

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-10 2144  ax-11 2160  ax-12 2180

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1781  df-nf 1785  df-mo 2535

This theorem is referenced by:  mo3  2559  nfeu1ALT  2584  moanmo  2617  moexexlem  2621  mopick2  2632  2mo  2643  2eu3  2649  nfrmo1  3373  mob  3671  morex  3673  wl-mo3t  37620  permaxrep  45109