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Theorem bnj836 32897
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj836.1  |-  ( et  <->  (
ph  /\  ps  /\  ch ) )
bnj836.2  |-  ( ps 
->  ta )
Assertion
Ref Expression
bnj836  |-  ( et 
->  ta )

Proof of Theorem bnj836
StepHypRef Expression
1 bnj836.1 . 2  |-  ( et  <->  (
ph  /\  ps  /\  ch ) )
2 bnj836.2 . . 3  |-  ( ps 
->  ta )
323ad2ant2 1018 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ta )
41, 3sylbi 195 1  |-  ( et 
->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ w3a 973
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 185  df-an 371  df-3an 975
This theorem is referenced by:  bnj1379  32968  bnj1175  33139  bnj1286  33154  bnj1450  33185  bnj1501  33202  bnj1523  33206
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