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

Theorem jctild 316
Description: Deduction conjoining a theorem to left of consequent in an implication. (Contributed by NM, 21-Apr-2005.)
Hypotheses
Ref Expression
jctild.1 (𝜑 → (𝜓𝜒))
jctild.2 (𝜑𝜃)
Assertion
Ref Expression
jctild (𝜑 → (𝜓 → (𝜃𝜒)))

Proof of Theorem jctild
StepHypRef Expression
1 jctild.2 . . 3 (𝜑𝜃)
21a1d 22 . 2 (𝜑 → (𝜓𝜃))
3 jctild.1 . 2 (𝜑 → (𝜓𝜒))
42, 3jcad 307 1 (𝜑 → (𝜓 → (𝜃𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108
This theorem is referenced by:  anc2li  329  syl6an  1434  poxp  6230  ssenen  6848  aptiprleml  7635  zmulcl  9302  rexuz3  10992  cau3lem  11116  gcdzeq  12015  isprm3  12110  epttop  13461  lmtopcnp  13621  txcnp  13642
  Copyright terms: Public domain W3C validator