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Theorem nfmo1 2154
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 2148 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1706 . . 3  |-  F/ x E. x ph
3 nfeu1 2153 . . 3  |-  F/ x E! x ph
42, 3nfim 1769 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1557 1  |-  F/ x E* x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1528   F/wnf 1531   E!weu 2143   E*wmo 2144
This theorem is referenced by:  moanmo  2203  mopick2  2210  moexex  2212  2eu3  2225  nfrmo1  2711  mob  2947  morex  2949
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-eu 2147  df-mo 2148
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