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Theorem bnj951 29123
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj951.1  |-  ( ta 
->  ph )
bnj951.2  |-  ( ta 
->  ps )
bnj951.3  |-  ( ta 
->  ch )
bnj951.4  |-  ( ta 
->  th )
Assertion
Ref Expression
bnj951  |-  ( ta 
->  ( ph  /\  ps  /\ 
ch  /\  th )
)

Proof of Theorem bnj951
StepHypRef Expression
1 bnj951.1 . . 3  |-  ( ta 
->  ph )
2 bnj951.2 . . 3  |-  ( ta 
->  ps )
3 bnj951.3 . . 3  |-  ( ta 
->  ch )
41, 2, 33jca 1132 . 2  |-  ( ta 
->  ( ph  /\  ps  /\ 
ch ) )
5 bnj951.4 . 2  |-  ( ta 
->  th )
6 df-bnj17 29028 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  ch )  /\  th ) )
74, 5, 6sylanbrc 645 1  |-  ( ta 
->  ( ph  /\  ps  /\ 
ch  /\  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934    /\ w-bnj17 29027
This theorem is referenced by:  bnj966  29292  bnj967  29293  bnj910  29296  bnj1006  29307  bnj1118  29330  bnj1177  29352
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 29028
  Copyright terms: Public domain W3C validator