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Theorem hbmo 2016
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
hbmo.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
hbmo  |-  ( E* y ph  ->  A. x E* y ph )

Proof of Theorem hbmo
StepHypRef Expression
1 df-mo 1981 . 2  |-  ( E* y ph  <->  ( E. y ph  ->  E! y ph ) )
2 hbmo.1 . . . 4  |-  ( ph  ->  A. x ph )
32hbex 1600 . . 3  |-  ( E. y ph  ->  A. x E. y ph )
42hbeu 1998 . . 3  |-  ( E! y ph  ->  A. x E! y ph )
53, 4hbim 1509 . 2  |-  ( ( E. y ph  ->  E! y ph )  ->  A. x ( E. y ph  ->  E! y ph ) )
61, 5hbxfrbi 1433 1  |-  ( E* y ph  ->  A. x E* y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314   E.wex 1453   E!weu 1977   E*wmo 1978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-eu 1980  df-mo 1981
This theorem is referenced by:  moexexdc  2061  2moex  2063  2euex  2064  2exeu  2069
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