Theorem nfmo1 2640

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 2622	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfa1 2155	. . 3 ⊢ Ⅎ𝑥∀𝑥(𝜑 → 𝑥 = 𝑦)
3	2	nfex 2343	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
4	1, 3	nfxfr 1853	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1535  ∃wex 1780  Ⅎwnf 1784  ∃*wmo 2620

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 1970  ax-7 2015  ax-10 2145  ax-11 2161  ax-12 2177

This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1781  df-nf 1785  df-mo 2622

This theorem is referenced by:  mo3  2647  nfeu1ALT  2674  moanmo  2706  moexexlem  2710  mopick2  2721  2mo  2732  2eu3  2737  nfrmo1  3366  mob  3694  morex  3696  wl-mo3t  34841