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Theorem pm5.53 803
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 790 . 2  |-  ( ( ( ( ph  \/  ps )  \/  ch )  ->  th )  <->  ( (
( ph  \/  ps )  ->  th )  /\  ( ch  ->  th ) ) )
2 jaob 790 . . 3  |-  ( ( ( ph  \/  ps )  ->  th )  <->  ( ( ph  ->  th )  /\  ( ps  ->  th ) ) )
32anbi1i 699 . 2  |-  ( ( ( ( ph  \/  ps )  ->  th )  /\  ( ch  ->  th )
)  <->  ( ( (
ph  ->  th )  /\  ( ps  ->  th ) )  /\  ( ch  ->  th )
) )
41, 3bitri 252 1  |-  ( ( ( ( ph  \/  ps )  \/  ch )  ->  th )  <->  ( (
( ph  ->  th )  /\  ( ps  ->  th )
)  /\  ( ch  ->  th ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    \/ wo 369    /\ wa 370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372
This theorem is referenced by: (None)
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