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Theorem simp2bi 955
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
simp2bi  |-  ( ph  ->  ch )

Proof of Theorem simp2bi
StepHypRef Expression
1 3simp1bi.1 . . 3  |-  ( ph  <->  ( ps  /\  ch  /\  th ) )
21biimpi 118 . 2  |-  ( ph  ->  ( ps  /\  ch  /\ 
th ) )
32simp2d 952 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  0ellim  4181  smodm  5960  erdm  6203  dif1en  6435  eluzelz  8761  elfz3nn0  9260
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