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

Theorem jctild 314
Description: Deduction conjoining a theorem to left of consequent in an implication. (Contributed by NM, 21-Apr-2005.)
Hypotheses
Ref Expression
jctild.1  |-  ( ph  ->  ( ps  ->  ch ) )
jctild.2  |-  ( ph  ->  th )
Assertion
Ref Expression
jctild  |-  ( ph  ->  ( ps  ->  ( th  /\  ch ) ) )

Proof of Theorem jctild
StepHypRef Expression
1 jctild.2 . . 3  |-  ( ph  ->  th )
21a1d 22 . 2  |-  ( ph  ->  ( ps  ->  th )
)
3 jctild.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3jcad 305 1  |-  ( ph  ->  ( ps  ->  ( th  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107
This theorem is referenced by:  anc2li  327  syl6an  1427  poxp  6209  ssenen  6826  aptiprleml  7590  zmulcl  9254  rexuz3  10943  cau3lem  11067  gcdzeq  11966  isprm3  12061  epttop  12845  lmtopcnp  13005  txcnp  13026
  Copyright terms: Public domain W3C validator