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Theorem nfmo1 2167
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 2161 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1718 . . 3  |-  F/ x E. x ph
3 nfeu1 2166 . . 3  |-  F/ x E! x ph
42, 3nfim 1781 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1560 1  |-  F/ x E* x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1531   F/wnf 1534   E!weu 2156   E*wmo 2157
This theorem is referenced by:  moanmo  2216  mopick2  2223  moexex  2225  2eu3  2238  nfrmo1  2724  mob  2960  morex  2962
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-eu 2160  df-mo 2161
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