ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl7bi Unicode version

Theorem syl7bi 164
Description: A mixed syllogism inference from a doubly nested implication and a biconditional. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
syl7bi.1  |-  ( ph  <->  ps )
syl7bi.2  |-  ( ch 
->  ( th  ->  ( ps  ->  ta ) ) )
Assertion
Ref Expression
syl7bi  |-  ( ch 
->  ( th  ->  ( ph  ->  ta ) ) )

Proof of Theorem syl7bi
StepHypRef Expression
1 syl7bi.1 . . 3  |-  ( ph  <->  ps )
21biimpi 119 . 2  |-  ( ph  ->  ps )
3 syl7bi.2 . 2  |-  ( ch 
->  ( th  ->  ( ps  ->  ta ) ) )
42, 3syl7 69 1  |-  ( ch 
->  ( th  ->  ( ph  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  necon1addc  2385  necon1ddc  2387  rspct  2785  2reuswapdc  2891  nn0lt2  9155  fzofzim  9995  ndvdssub  11661  bj-findis  13346
  Copyright terms: Public domain W3C validator