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

Theorem bigolden 922
Description: Dijkstra-Scholten's Golden Rule for calculational proofs. (Contributed by NM, 10-Jan-2005.)
Assertion
Ref Expression
bigolden  |-  ( ( ( ph  /\  ps ) 
<-> 
ph )  <->  ( ps  <->  (
ph  \/  ps )
) )

Proof of Theorem bigolden
StepHypRef Expression
1 pm4.71 384 . 2  |-  ( (
ph  ->  ps )  <->  ( ph  <->  (
ph  /\  ps )
) )
2 pm4.72 795 . 2  |-  ( (
ph  ->  ps )  <->  ( ps  <->  (
ph  \/  ps )
) )
3 bicom 139 . 2  |-  ( (
ph 
<->  ( ph  /\  ps ) )  <->  ( ( ph  /\  ps )  <->  ph ) )
41, 2, 33bitr3ri 210 1  |-  ( ( ( ph  /\  ps ) 
<-> 
ph )  <->  ( ps  <->  (
ph  \/  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104    \/ wo 680
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator