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Theorem simp3bi 960
Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
3simp1bi.1  |-  ( ph  <->  ( ps  /\  ch  /\  th ) )
Assertion
Ref Expression
simp3bi  |-  ( ph  ->  th )

Proof of Theorem simp3bi
StepHypRef Expression
1 3simp1bi.1 . . 3  |-  ( ph  <->  ( ps  /\  ch  /\  th ) )
21biimpi 118 . 2  |-  ( ph  ->  ( ps  /\  ch  /\ 
th ) )
32simp3d 957 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    /\ w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 926
This theorem is referenced by:  limuni  4223  smores2  6059  ersym  6302  ertr  6305  fiintim  6637  eluzle  9029  ef01bndlem  11043  sin01bnd  11044  cos01bnd  11045  sin01gt0  11048
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