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

Theorem condcOLD 840
Description: Obsolete proof of condc 839 as of 18-Nov-2023. (Contributed by Jim Kingdon, 13-Mar-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
condcOLD  |-  (DECID  ph  ->  ( ( -.  ph  ->  -. 
ps )  ->  ( ps  ->  ph ) ) )

Proof of Theorem condcOLD
StepHypRef Expression
1 df-dc 821 . 2  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 ax-1 6 . . . 4  |-  ( ph  ->  ( ps  ->  ph )
)
32a1d 22 . . 3  |-  ( ph  ->  ( ( -.  ph  ->  -.  ps )  -> 
( ps  ->  ph )
) )
4 pm2.27 40 . . . 4  |-  ( -. 
ph  ->  ( ( -. 
ph  ->  -.  ps )  ->  -.  ps ) )
5 ax-in2 605 . . . 4  |-  ( -. 
ps  ->  ( ps  ->  ph ) )
64, 5syl6 33 . . 3  |-  ( -. 
ph  ->  ( ( -. 
ph  ->  -.  ps )  ->  ( ps  ->  ph )
) )
73, 6jaoi 706 . 2  |-  ( (
ph  \/  -.  ph )  ->  ( ( -.  ph  ->  -.  ps )  -> 
( ps  ->  ph )
) )
81, 7sylbi 120 1  |-  (DECID  ph  ->  ( ( -.  ph  ->  -. 
ps )  ->  ( ps  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 698  DECID wdc 820
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-dc 821
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator