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Theorem pm5.53 749
Description: Theorem *5.53 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.53  |-  ( ( ( ( ph  \/  ps )  \/  ch )  ->  th )  <->  ( (
( ph  ->  th )  /\  ( ps  ->  th )
)  /\  ( ch  ->  th ) ) )

Proof of Theorem pm5.53
StepHypRef Expression
1 jaob 664 . 2  |-  ( ( ( ( ph  \/  ps )  \/  ch )  ->  th )  <->  ( (
( ph  \/  ps )  ->  th )  /\  ( ch  ->  th ) ) )
2 jaob 664 . . 3  |-  ( ( ( ph  \/  ps )  ->  th )  <->  ( ( ph  ->  th )  /\  ( ps  ->  th ) ) )
32anbi1i 446 . 2  |-  ( ( ( ( ph  \/  ps )  ->  th )  /\  ( ch  ->  th )
)  <->  ( ( (
ph  ->  th )  /\  ( ps  ->  th ) )  /\  ( ch  ->  th )
) )
41, 3bitri 182 1  |-  ( ( ( ( ph  \/  ps )  \/  ch )  ->  th )  <->  ( (
( ph  ->  th )  /\  ( ps  ->  th )
)  /\  ( ch  ->  th ) ) )
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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