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Theorem nfmo1 2282
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 2273 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1784 . . 3  |-  F/ x E. x ph
3 nfeu1 2281 . . 3  |-  F/ x E! x ph
42, 3nfim 1862 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1620 1  |-  F/ x E* x ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1591   F/wnf 1594   E!weu 2268   E*wmo 2269
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798
This theorem depends on definitions:  df-bi 185  df-ex 1592  df-nf 1595  df-eu 2272  df-mo 2273
This theorem is referenced by:  mo3  2313  moanmo  2350  mopick2  2363  moexex  2364  moexexOLD  2365  2mo  2375  2moOLD  2376  2eu3  2382  nfrmo1  3026  mob  3278  morex  3280  wl-mo3t  29448
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