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Theorem nfmo1 2274
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 2265 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1780 . . 3  |-  F/ x E. x ph
3 nfeu1 2273 . . 3  |-  F/ x E! x ph
42, 3nfim 1855 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1616 1  |-  F/ x E* x ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1587   F/wnf 1590   E!weu 2260   E*wmo 2261
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588  df-nf 1591  df-eu 2264  df-mo 2265
This theorem is referenced by:  mo3  2305  moanmo  2342  mopick2  2355  moexex  2356  moexexOLD  2357  2mo  2367  2moOLD  2368  2eu3  2374  nfrmo1  2990  mob  3240  morex  3242  wl-mo3t  28537
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