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Theorem pm4.39 843
Description: Theorem *4.39 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.39  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ( ph  \/  ps )  <->  ( ch  \/  th ) ) )

Proof of Theorem pm4.39
StepHypRef Expression
1 simpl 445 . 2  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ph  <->  ch ) )
2 simpr 449 . 2  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ps  <->  th ) )
31, 2orbi12d 692 1  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ( ph  \/  ps )  <->  ( ch  \/  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    \/ wo 359    /\ wa 360
This theorem is referenced by:  3orbi123VD  27896
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  df-an 362
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