ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  hbeu1 Unicode version

Theorem hbeu1 2036
Description: Bound-variable hypothesis builder for uniqueness. (Contributed by NM, 9-Jul-1994.)
Assertion
Ref Expression
hbeu1  |-  ( E! x ph  ->  A. x E! x ph )

Proof of Theorem hbeu1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-eu 2029 . 2  |-  ( E! x ph  <->  E. y A. x ( ph  <->  x  =  y ) )
2 hba1 1540 . . 3  |-  ( A. x ( ph  <->  x  =  y )  ->  A. x A. x ( ph  <->  x  =  y ) )
32hbex 1636 . 2  |-  ( E. y A. x (
ph 
<->  x  =  y )  ->  A. x E. y A. x ( ph  <->  x  =  y ) )
41, 3hbxfrbi 1472 1  |-  ( E! x ph  ->  A. x E! x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105   A.wal 1351   E.wex 1492   E!weu 2026
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117  df-eu 2029
This theorem is referenced by:  hbmo1  2064  eupicka  2106  exists2  2123
  Copyright terms: Public domain W3C validator