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Theorem bnj769 29108
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj769.1  |-  ( et  <->  (
ph  /\  ps  /\  ch  /\ 
th ) )
bnj769.2  |-  ( ph  ->  ta )
Assertion
Ref Expression
bnj769  |-  ( et 
->  ta )

Proof of Theorem bnj769
StepHypRef Expression
1 bnj769.1 . 2  |-  ( et  <->  (
ph  /\  ps  /\  ch  /\ 
th ) )
2 bnj769.2 . . 3  |-  ( ph  ->  ta )
32bnj705 29098 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  ->  ta )
41, 3sylbi 187 1  |-  ( et 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ w-bnj17 29027
This theorem is referenced by:  bnj966  29292  bnj967  29293  bnj986  29302  bnj1053  29322  bnj1030  29333  bnj1133  29335  bnj1450  29396
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