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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 𝑥∃*𝑥𝜑

Proof of Theorem nfmo1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-mo 2535 . 2 (∃*𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 2149 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 2318 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1856 1 𝑥∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540  wex 1782  wnf 1786  ∃*wmo 2533
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2138  ax-11 2155  ax-12 2172
This theorem depends on definitions:  df-bi 206  df-or 847  df-ex 1783  df-nf 1787  df-mo 2535
This theorem is referenced by:  mo3  2559  nfeu1ALT  2584  moanmo  2619  moexexlem  2623  mopick2  2634  2mo  2645  2eu3  2650  nfrmo1  3408  mob  3714  morex  3716  wl-mo3t  36441
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