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Theorem bnj290 29074
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj290  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ch  /\  th  /\  ps ) )

Proof of Theorem bnj290
StepHypRef Expression
1 3anrot 941 . . 3  |-  ( ( ps  /\  ch  /\  th )  <->  ( ch  /\  th 
/\  ps ) )
21anbi2i 676 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  <->  ( ph  /\  ( ch  /\  th  /\  ps ) ) )
3 bnj252 29067 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\  ( ps  /\  ch  /\ 
th ) ) )
4 bnj252 29067 . 2  |-  ( (
ph  /\  ch  /\  th  /\  ps )  <->  ( ph  /\  ( ch  /\  th  /\  ps ) ) )
52, 3, 43bitr4i 269 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ch  /\  th  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    /\ w3a 936    /\ w-bnj17 29050
This theorem is referenced by:  bnj291  29075  bnj334  29077
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 178  df-an 361  df-3an 938  df-bnj17 29051
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