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Theorem nfmo1 2241
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 2233 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1858 . . 3  |-  F/ x E. x ph
3 nfeu1 2240 . . 3  |-  F/ x E! x ph
42, 3nfim 1938 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1660 1  |-  F/ x E* x ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1627   F/wnf 1631   E!weu 2228   E*wmo 2229
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1633  ax-4 1646  ax-5 1719  ax-6 1765  ax-7 1808  ax-10 1855  ax-11 1860  ax-12 1872
This theorem depends on definitions:  df-bi 185  df-ex 1628  df-nf 1632  df-eu 2232  df-mo 2233
This theorem is referenced by:  mo3  2268  moanmo  2294  mopick2  2303  moexex  2304  2mo  2314  2moOLD  2315  2eu3  2320  nfrmo1  2967  mob  3219  morex  3221  wl-mo3t  30222
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