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Theorem nfmo1 2629
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfmo1 𝑥∃*𝑥𝜑

Proof of Theorem nfmo1
StepHypRef Expression
1 df-mo 2623 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2 nfe1 2183 . . 3 𝑥𝑥𝜑
3 nfeu1 2628 . . 3 𝑥∃!𝑥𝜑
42, 3nfim 1977 . 2 𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
51, 4nfxfr 1929 1 𝑥∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1852  wnf 1856  ∃!weu 2618  ∃*wmo 2619
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-11 2190  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-ex 1853  df-nf 1858  df-eu 2622  df-mo 2623
This theorem is referenced by:  mo3  2656  moanmo  2681  mopick2  2689  moexex  2690  2mo  2700  2eu3  2704  nfrmo1  3259  mob  3540  morex  3542  wl-mo3t  33688
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