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Theorem pm4.38 842
Description: Theorem *4.38 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.38  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ( ph  /\  ps )  <->  ( ch  /\ 
th ) ) )

Proof of Theorem pm4.38
StepHypRef Expression
1 simpl 443 . 2  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ph  <->  ch ) )
2 simpr 447 . 2  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ps  <->  th ) )
31, 2anbi12d 691 1  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ( ph  /\  ps )  <->  ( ch  /\ 
th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  xpf1o  7023  isprm3  12767  csbingVD  28033  csbxpgVD  28043  csbunigVD  28047
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-an 360
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