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

Theorem sylcom 28
Description: Syllogism inference with commutation of antecedents. (Contributed by NM, 29-Aug-2004.) (Proof shortened by O'Cat, 2-Feb-2006.) (Proof shortened by Stefan Allan, 23-Feb-2006.)
Hypotheses
Ref Expression
sylcom.1  |-  ( ph  ->  ( ps  ->  ch ) )
sylcom.2  |-  ( ps 
->  ( ch  ->  th )
)
Assertion
Ref Expression
sylcom  |-  ( ph  ->  ( ps  ->  th )
)

Proof of Theorem sylcom
StepHypRef Expression
1 sylcom.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 sylcom.2 . . 3  |-  ( ps 
->  ( ch  ->  th )
)
32a2i 11 . 2  |-  ( ( ps  ->  ch )  ->  ( ps  ->  th )
)
41, 3syl 14 1  |-  ( ph  ->  ( ps  ->  th )
)
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:  syl5com  29  syl6  33  syli  37  mpbidi  150  con4biddc  793  jaddc  800  con1biddc  809  necon4addc  2326  necon4bddc  2327  necon4ddc  2328  necon1addc  2332  necon1bddc  2333  dmcosseq  4719  iss  4773  funopg  5063  snon0  6701
  Copyright terms: Public domain W3C validator