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Theorem nfmo1 2570
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 2565 . 2 (∃*𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 2193 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 2327 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1948 1 𝑥∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650  wex 1874  wnf 1878  ∃*wmo 2563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-10 2183  ax-11 2198  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-or 874  df-ex 1875  df-nf 1879  df-mo 2565
This theorem is referenced by:  nfeu1ALT  2586  mo3  2628  moanmo  2654  mopick2  2662  moexex  2663  2mo  2673  2eu3  2677  nfrmo1  3258  mob  3547  morex  3549  wl-mo3t  33783
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