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Theorem pm5.55 872
Description: Theorem *5.55 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 20-Jan-2013.)
Assertion
Ref Expression
pm5.55  |-  ( ( ( ph  \/  ps ) 
<-> 
ph )  \/  (
( ph  \/  ps ) 
<->  ps ) )

Proof of Theorem pm5.55
StepHypRef Expression
1 biort 871 . . . . 5  |-  ( ph  ->  ( ph  <->  ( ph  \/  ps ) ) )
21bicomd 194 . . . 4  |-  ( ph  ->  ( ( ph  \/  ps )  <->  ph ) )
3 biorf 396 . . . . 5  |-  ( -. 
ph  ->  ( ps  <->  ( ph  \/  ps ) ) )
43bicomd 194 . . . 4  |-  ( -. 
ph  ->  ( ( ph  \/  ps )  <->  ps )
)
52, 4nsyl4 136 . . 3  |-  ( -.  ( ( ph  \/  ps )  <->  ps )  ->  (
( ph  \/  ps ) 
<-> 
ph ) )
65con1i 123 . 2  |-  ( -.  ( ( ph  \/  ps )  <->  ph )  ->  (
( ph  \/  ps ) 
<->  ps ) )
76orri 367 1  |-  ( ( ( ph  \/  ps ) 
<-> 
ph )  \/  (
( ph  \/  ps ) 
<->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178    \/ wo 359
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361
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