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

Theorem biimt 230
Description: A wff is equivalent to itself with true antecedent. (Contributed by NM, 28-Jan-1996.)
Assertion
Ref Expression
biimt  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )

Proof of Theorem biimt
StepHypRef Expression
1 ax-1 5 . 2  |-  ( ps 
->  ( ph  ->  ps ) )
2 pm2.27 35 . 2  |-  ( ph  ->  ( ( ph  ->  ps )  ->  ps )
)
31, 2impbid2 131 1  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.5  231  a1bi  232  abai  494  dedlem0a  875  ceqsralt  2581  reu8  2737  csbiebt  2886  r19.3rm  3310  fncnv  4965  ovmpt2dxf  5626  brecop  6196
  Copyright terms: Public domain W3C validator