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Theorem hbmo 2014
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 1979 . 2  |-  ( E* y ph  <->  ( E. y ph  ->  E! y ph ) )
2 hbmo.1 . . . 4  |-  ( ph  ->  A. x ph )
32hbex 1598 . . 3  |-  ( E. y ph  ->  A. x E. y ph )
42hbeu 1996 . . 3  |-  ( E! y ph  ->  A. x E! y ph )
53, 4hbim 1507 . 2  |-  ( ( E. y ph  ->  E! y ph )  ->  A. x ( E. y ph  ->  E! y ph ) )
61, 5hbxfrbi 1431 1  |-  ( E* y ph  ->  A. x E* y 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-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979
This theorem is referenced by:  moexexdc  2059  2moex  2061  2euex  2062  2exeu  2067
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