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Theorem nfmo1 2038
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 2030 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2 nfe1 1496 . . 3 𝑥𝑥𝜑
3 nfeu1 2037 . . 3 𝑥∃!𝑥𝜑
42, 3nfim 1572 . 2 𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
51, 4nfxfr 1474 1 𝑥∃*𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1460  wex 1492  ∃!weu 2026  ∃*wmo 2027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-eu 2029  df-mo 2030
This theorem is referenced by:  moanmo  2103  euexex  2111  nfrmo1  2649  mob  2919  morex  2921  funimaexglem  5299
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