ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp2bi Unicode version

Theorem simp2bi 920
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 113 . 2  |-  ( ph  ->  ( ps  /\  ch  /\ 
th ) )
32simp2d 917 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98    /\ w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  0ellim  4135  smodm  5906  erdm  6116  dif1en  6337  eluzelz  8482  elfz3nn0  8976
  Copyright terms: Public domain W3C validator