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Theorem nfmo1 2634
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 𝑥∃*𝑥𝜑

Proof of Theorem nfmo1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-mo 2615 . 2 (∃*𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 2146 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 2334 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1844 1 𝑥∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526  wex 1771  wnf 1775  ∃*wmo 2613
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-10 2136  ax-11 2151  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-or 842  df-ex 1772  df-nf 1776  df-mo 2615
This theorem is referenced by:  mo3  2641  nfeu1ALT  2668  moanmo  2700  moexexlem  2704  mopick2  2715  2mo  2726  2eu3  2732  2eu3OLD  2733  nfrmo1  3369  mob  3705  morex  3707  wl-mo3t  34693
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