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Theorem hbmo1 2013
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 8-Mar-1995.)
Assertion
Ref Expression
hbmo1  |-  ( E* x ph  ->  A. x E* x ph )

Proof of Theorem hbmo1
StepHypRef Expression
1 df-mo 1979 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 hbe1 1454 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
3 hbeu1 1985 . . 3  |-  ( E! x ph  ->  A. x E! x ph )
42, 3hbim 1507 . 2  |-  ( ( E. x ph  ->  E! x ph )  ->  A. x ( E. x ph  ->  E! x ph ) )
51, 4hbxfrbi 1431 1  |-  ( E* x ph  ->  A. x E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1312   E.wex 1451   E!weu 1975   E*wmo 1976
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-eu 1978  df-mo 1979
This theorem is referenced by:  mopick2  2058  moexexdc  2059
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