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Theorem bnj833 28788
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj833.1  |-  ( et  <->  (
ph  /\  ps )
)
bnj833.2  |-  ( ps 
->  ta )
Assertion
Ref Expression
bnj833  |-  ( et 
->  ta )

Proof of Theorem bnj833
StepHypRef Expression
1 bnj833.1 . 2  |-  ( et  <->  (
ph  /\  ps )
)
2 bnj833.2 . . 3  |-  ( ps 
->  ta )
32adantl 452 . 2  |-  ( (
ph  /\  ps )  ->  ta )
41, 3sylbi 187 1  |-  ( et 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  bnj570  28937  bnj1145  29023  bnj1398  29064  bnj1442  29079
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
  Copyright terms: Public domain W3C validator