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Theorem nfmo1 2250
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 2244 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1739 . . 3  |-  F/ x E. x ph
3 nfeu1 2249 . . 3  |-  F/ x E! x ph
42, 3nfim 1822 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1576 1  |-  F/ x E* x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1547   F/wnf 1550   E!weu 2239   E*wmo 2240
This theorem is referenced by:  moanmo  2299  mopick2  2306  moexex  2308  2eu3  2321  nfrmo1  2823  mob  3060  morex  3062
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-ex 1548  df-nf 1551  df-eu 2243  df-mo 2244
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