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Theorem bnj771 29133
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj771.1  |-  ( et  <->  (
ph  /\  ps  /\  ch  /\ 
th ) )
bnj771.2  |-  ( ch 
->  ta )
Assertion
Ref Expression
bnj771  |-  ( et 
->  ta )

Proof of Theorem bnj771
StepHypRef Expression
1 bnj771.1 . 2  |-  ( et  <->  (
ph  /\  ps  /\  ch  /\ 
th ) )
2 bnj771.2 . . 3  |-  ( ch 
->  ta )
32bnj707 29123 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  ->  ta )
41, 3sylbi 188 1  |-  ( et 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ w-bnj17 29050
This theorem is referenced by:  bnj1247  29180  bnj996  29326  bnj1097  29350  bnj1145  29362  bnj1259  29385  bnj1296  29390  bnj1450  29419
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
  Copyright terms: Public domain W3C validator