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Theorem hbmo 1984
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 1949 . 2  |-  ( E* y ph  <->  ( E. y ph  ->  E! y ph ) )
2 hbmo.1 . . . 4  |-  ( ph  ->  A. x ph )
32hbex 1570 . . 3  |-  ( E. y ph  ->  A. x E. y ph )
42hbeu 1966 . . 3  |-  ( E! y ph  ->  A. x E! y ph )
53, 4hbim 1480 . 2  |-  ( ( E. y ph  ->  E! y ph )  ->  A. x ( E. y ph  ->  E! y ph ) )
61, 5hbxfrbi 1404 1  |-  ( E* y ph  ->  A. x E* y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1285   E.wex 1424   E!weu 1945   E*wmo 1946
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-eu 1948  df-mo 1949
This theorem is referenced by:  moexexdc  2029  2moex  2031  2euex  2032  2exeu  2037
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