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Theorem hbmo 1982
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 1947 . 2  |-  ( E* y ph  <->  ( E. y ph  ->  E! y ph ) )
2 hbmo.1 . . . 4  |-  ( ph  ->  A. x ph )
32hbex 1568 . . 3  |-  ( E. y ph  ->  A. x E. y ph )
42hbeu 1964 . . 3  |-  ( E! y ph  ->  A. x E! y ph )
53, 4hbim 1478 . 2  |-  ( ( E. y ph  ->  E! y ph )  ->  A. x ( E. y ph  ->  E! y ph ) )
61, 5hbxfrbi 1402 1  |-  ( E* y ph  ->  A. x E* y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   E.wex 1422   E!weu 1943   E*wmo 1944
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947
This theorem is referenced by:  moexexdc  2027  2moex  2029  2euex  2030  2exeu  2035
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