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Theorem bnj312 29305
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj312  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ps  /\ 
ph  /\  ch  /\  th ) )

Proof of Theorem bnj312
StepHypRef Expression
1 3ancoma 989 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
21anbi1i 699 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th ) 
<->  ( ( ps  /\  ph 
/\  ch )  /\  th ) )
3 df-bnj17 29280 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  ch )  /\  th ) )
4 df-bnj17 29280 . 2  |-  ( ( ps  /\  ph  /\  ch  /\  th )  <->  ( ( ps  /\  ph  /\  ch )  /\  th ) )
52, 3, 43bitr4i 280 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ps  /\ 
ph  /\  ch  /\  th ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    /\ wa 370    /\ w3a 982    /\ w-bnj17 29279
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 188  df-an 372  df-3an 984  df-bnj17 29280
This theorem is referenced by:  bnj334  29306  bnj563  29341  bnj953  29538
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