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Theorem pm4.38 867
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 457 . 2  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ph  <->  ch ) )
2 simpr 461 . 2  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ps  <->  th ) )
31, 2anbi12d 710 1  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ( ph  /\  ps )  <->  ( ch  /\ 
th ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  xpf1o  7494  isprm3  13793  csbingVD  31716  csbxpgVD  31726  csbunigVD  31730
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