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Theorem pm4.38 572
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 107 . 2  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ph  <->  ch ) )
2 simpr 108 . 2  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ps  <->  th ) )
31, 2anbi12d 457 1  |-  ( ( ( ph  <->  ch )  /\  ( ps  <->  th )
)  ->  ( ( ph  /\  ps )  <->  ( ch  /\ 
th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  xpf1o  6540  isprm3  11193
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