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Theorem bnj250 28726
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj250  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\  ( ( ps  /\  ch )  /\  th )
) )

Proof of Theorem bnj250
StepHypRef Expression
1 df-bnj17 28712 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  ch )  /\  th ) )
2 3anass 938 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ( ps  /\  ch ) ) )
32anbi1i 676 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th ) 
<->  ( ( ph  /\  ( ps  /\  ch )
)  /\  th )
)
4 anass 630 . 2  |-  ( ( ( ph  /\  ( ps  /\  ch ) )  /\  th )  <->  ( ph  /\  ( ( ps  /\  ch )  /\  th )
) )
51, 3, 43bitri 262 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\  ( ( ps  /\  ch )  /\  th )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    /\ w3a 934    /\ w-bnj17 28711
This theorem is referenced by:  bnj251  28727  bnj252  28728  bnj345  28739
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
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