ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3anim1i Unicode version

Theorem 3anim1i 1101
Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)
Hypothesis
Ref Expression
3animi.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
3anim1i  |-  ( (
ph  /\  ch  /\  th )  ->  ( ps  /\  ch  /\  th ) )

Proof of Theorem 3anim1i
StepHypRef Expression
1 3animi.1 . 2  |-  ( ph  ->  ps )
2 id 19 . 2  |-  ( ch 
->  ch )
3 id 19 . 2  |-  ( th 
->  th )
41, 2, 33anim123i 1100 1  |-  ( (
ph  /\  ch  /\  th )  ->  ( ps  /\  ch  /\  th ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  syl3an1  1179  syl3anl1  1194  syl3anr1  1198  elioc2  8906  elico2  8907  elicc2  8908  dvdsleabs2  10158
  Copyright terms: Public domain W3C validator