Theorem nfmo1 2558

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 2541	. 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦))
2		nfexa2 2184	. 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)
3	1, 2	nfxfr 1855	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1781  Ⅎwnf 1785  ∃*wmo 2538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-10 2147  ax-11 2163

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-nf 1786  df-mo 2540

This theorem is referenced by:  mo3  2565  nfeu1  2590  moanmo  2623  moexexlem  2627  mopick2  2638  2mo  2649  2eu3  2655  nfrmo1  3379  mob  3677  morex  3679  wl-mo3t  37831  permaxrep  45362