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Theorem bigolden 901
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 pm4.71 611 . 2  |-  ( (
ph  ->  ps )  <->  ( ph  <->  (
ph  /\  ps )
) )
2 pm4.72 846 . 2  |-  ( (
ph  ->  ps )  <->  ( ps  <->  (
ph  \/  ps )
) )
3 bicom 191 . 2  |-  ( (
ph 
<->  ( ph  /\  ps ) )  <->  ( ( ph  /\  ps )  <->  ph ) )
41, 2, 33bitr3ri 267 1  |-  ( ( ( ph  /\  ps ) 
<-> 
ph )  <->  ( ps  <->  (
ph  \/  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    \/ wo 357    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
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