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Theorem nfmo1 2555
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 2538 . 2 (∃*𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 2149 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 2323 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1850 1 𝑥∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1535  wex 1776  wnf 1780  ∃*wmo 2536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-11 2155  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1777  df-nf 1781  df-mo 2538
This theorem is referenced by:  mo3  2562  nfeu1ALT  2587  moanmo  2620  moexexlem  2624  mopick2  2635  2mo  2646  2eu3  2652  nfrmo1  3409  mob  3726  morex  3728  wl-mo3t  37557
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