Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfmo1 Structured version   Visualization version   GIF version

Theorem nfmo1 2637
 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 2618 . 2 (∃*𝑥𝜑 ↔ ∃𝑦𝑥(𝜑𝑥 = 𝑦))
2 nfa1 2151 . . 3 𝑥𝑥(𝜑𝑥 = 𝑦)
32nfex 2339 . 2 𝑥𝑦𝑥(𝜑𝑥 = 𝑦)
41, 3nfxfr 1849 1 𝑥∃*𝑥𝜑
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1531  ∃wex 1776  Ⅎwnf 1780  ∃*wmo 2616 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 1907  ax-6 1966  ax-7 2011  ax-10 2141  ax-11 2157  ax-12 2173 This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1777  df-nf 1781  df-mo 2618 This theorem is referenced by:  mo3  2644  nfeu1ALT  2671  moanmo  2703  moexexlem  2707  mopick2  2718  2mo  2729  2eu3  2735  2eu3OLD  2736  nfrmo1  3371  mob  3707  morex  3709  wl-mo3t  34811
 Copyright terms: Public domain W3C validator