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Theorem bnj345 28739
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj345  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( th  /\  ph  /\  ps  /\  ch ) )

Proof of Theorem bnj345
StepHypRef Expression
1 bnj334 28738 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
ph  /\  ps  /\  th ) )
2 bnj250 28726 . . 3  |-  ( ( ch  /\  ph  /\  ps  /\  th )  <->  ( ch  /\  ( ( ph  /\  ps )  /\  th )
) )
3 3anass 938 . . 3  |-  ( ( ch  /\  ( ph  /\ 
ps )  /\  th ) 
<->  ( ch  /\  (
( ph  /\  ps )  /\  th ) ) )
42, 3bitr4i 243 . 2  |-  ( ( ch  /\  ph  /\  ps  /\  th )  <->  ( ch  /\  ( ph  /\  ps )  /\  th ) )
5 3anrev 945 . . 3  |-  ( ( ch  /\  ( ph  /\ 
ps )  /\  th ) 
<->  ( th  /\  ( ph  /\  ps )  /\  ch ) )
6 bnj250 28726 . . . 4  |-  ( ( th  /\  ph  /\  ps  /\  ch )  <->  ( th  /\  ( ( ph  /\  ps )  /\  ch )
) )
7 3anass 938 . . . 4  |-  ( ( th  /\  ( ph  /\ 
ps )  /\  ch ) 
<->  ( th  /\  (
( ph  /\  ps )  /\  ch ) ) )
86, 7bitr4i 243 . . 3  |-  ( ( th  /\  ph  /\  ps  /\  ch )  <->  ( th  /\  ( ph  /\  ps )  /\  ch ) )
95, 8bitr4i 243 . 2  |-  ( ( ch  /\  ( ph  /\ 
ps )  /\  th ) 
<->  ( th  /\  ph  /\ 
ps  /\  ch )
)
101, 4, 93bitri 262 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( th  /\  ph  /\  ps  /\  ch ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    /\ w3a 934    /\ w-bnj17 28711
This theorem is referenced by:  bnj422  28740  bnj446  28742  bnj929  28968  bnj964  28975
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  df-3an 936  df-bnj17 28712
  Copyright terms: Public domain W3C validator