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Theorem hbmo1 1981
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 1947 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 hbe1 1425 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
3 hbeu1 1953 . . 3  |-  ( E! x ph  ->  A. x E! x ph )
42, 3hbim 1478 . 2  |-  ( ( E. x ph  ->  E! x ph )  ->  A. x ( E. x ph  ->  E! x ph ) )
51, 4hbxfrbi 1402 1  |-  ( E* x ph  ->  A. x E* x 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-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-eu 1946  df-mo 1947
This theorem is referenced by:  mopick2  2026  moexexdc  2027
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