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Theorem nfmo1 2279
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 2271 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1824 . . 3  |-  F/ x E. x ph
3 nfeu1 2278 . . 3  |-  F/ x E! x ph
42, 3nfim 1904 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1630 1  |-  F/ x E* x ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1597   F/wnf 1601   E!weu 2266   E*wmo 2267
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838
This theorem depends on definitions:  df-bi 185  df-ex 1598  df-nf 1602  df-eu 2270  df-mo 2271
This theorem is referenced by:  mo3  2307  moanmo  2337  mopick2  2346  moexex  2347  2mo  2357  2moOLD  2358  2eu3  2363  nfrmo1  3013  mob  3265  morex  3267  wl-mo3t  29989
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