ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl56 Unicode version

Theorem syl56 34
Description: Combine syl5 32 and syl6 33. (Contributed by NM, 14-Nov-2013.)
Hypotheses
Ref Expression
syl56.1  |-  ( ph  ->  ps )
syl56.2  |-  ( ch 
->  ( ps  ->  th )
)
syl56.3  |-  ( th 
->  ta )
Assertion
Ref Expression
syl56  |-  ( ch 
->  ( ph  ->  ta ) )

Proof of Theorem syl56
StepHypRef Expression
1 syl56.1 . 2  |-  ( ph  ->  ps )
2 syl56.2 . . 3  |-  ( ch 
->  ( ps  ->  th )
)
3 syl56.3 . . 3  |-  ( th 
->  ta )
42, 3syl6 33 . 2  |-  ( ch 
->  ( ps  ->  ta ) )
51, 4syl5 32 1  |-  ( ch 
->  ( ph  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  cbv2h  1675  euind  2780  reuind  2796  sbcimdv  2880  cores  4848  prnmaxl  6729  prnminu  6730
  Copyright terms: Public domain W3C validator