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Theorem bigolden 897
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 pm4.71 381 . 2  |-  ( (
ph  ->  ps )  <->  ( ph  <->  (
ph  /\  ps )
) )
2 pm4.72 770 . 2  |-  ( (
ph  ->  ps )  <->  ( ps  <->  (
ph  \/  ps )
) )
3 bicom 138 . 2  |-  ( (
ph 
<->  ( ph  /\  ps ) )  <->  ( ( ph  /\  ps )  <->  ph ) )
41, 2, 33bitr3ri 209 1  |-  ( ( ( ph  /\  ps ) 
<-> 
ph )  <->  ( ps  <->  (
ph  \/  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103    \/ wo 662
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-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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