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Theorem nfmo1 2009
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 2001 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2 nfe1 1472 . . 3 𝑥𝑥𝜑
3 nfeu1 2008 . . 3 𝑥∃!𝑥𝜑
42, 3nfim 1551 . 2 𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
51, 4nfxfr 1450 1 𝑥∃*𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1436  wex 1468  ∃!weu 1997  ∃*wmo 1998
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-eu 2000  df-mo 2001
This theorem is referenced by:  moanmo  2074  euexex  2082  nfrmo1  2601  mob  2861  morex  2863  funimaexglem  5201
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