ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl6c Unicode version

Theorem syl6c 64
Description: Inference combining syl6 33 with contraction. (Contributed by Alan Sare, 2-May-2011.)
Hypotheses
Ref Expression
syl6c.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl6c.2  |-  ( ph  ->  ( ps  ->  th )
)
syl6c.3  |-  ( ch 
->  ( th  ->  ta ) )
Assertion
Ref Expression
syl6c  |-  ( ph  ->  ( ps  ->  ta ) )

Proof of Theorem syl6c
StepHypRef Expression
1 syl6c.2 . 2  |-  ( ph  ->  ( ps  ->  th )
)
2 syl6c.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 syl6c.3 . . 3  |-  ( ch 
->  ( th  ->  ta ) )
42, 3syl6 33 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
51, 4mpdd 40 1  |-  ( ph  ->  ( ps  ->  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:  syldd  65  impbidd  122  jcad  295  dcbi  855  pm3.13dc  877  syl6ci  1350
  Copyright terms: Public domain W3C validator