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Theorem nfmo1 2031
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  |-  F/ x E* x ph

Proof of Theorem nfmo1
StepHypRef Expression
1 df-mo 2023 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1489 . . 3  |-  F/ x E. x ph
3 nfeu1 2030 . . 3  |-  F/ x E! x ph
42, 3nfim 1565 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1467 1  |-  F/ x E* x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1453   E.wex 1485   E!weu 2019   E*wmo 2020
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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527  ax-i5r 1528
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-eu 2022  df-mo 2023
This theorem is referenced by:  moanmo  2096  euexex  2104  nfrmo1  2642  mob  2912  morex  2914  funimaexglem  5281
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