ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  hbmo1 Unicode version

Theorem hbmo1 1983
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 1949 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 hbe1 1427 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
3 hbeu1 1955 . . 3  |-  ( E! x ph  ->  A. x E! x ph )
42, 3hbim 1480 . 2  |-  ( ( E. x ph  ->  E! x ph )  ->  A. x ( E. x ph  ->  E! x ph ) )
51, 4hbxfrbi 1404 1  |-  ( E* x ph  ->  A. x E* x 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-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-ial 1470  ax-i5r 1471
This theorem depends on definitions:  df-bi 115  df-eu 1948  df-mo 1949
This theorem is referenced by:  mopick2  2028  moexexdc  2029
  Copyright terms: Public domain W3C validator