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

Theorem jcai 309
Description: Deduction replacing implication with conjunction. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
jcai.1 (𝜑𝜓)
jcai.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
jcai (𝜑 → (𝜓𝜒))

Proof of Theorem jcai
StepHypRef Expression
1 jcai.1 . 2 (𝜑𝜓)
2 jcai.2 . . 3 (𝜑 → (𝜓𝜒))
31, 2mpd 13 . 2 (𝜑𝜒)
41, 3jca 304 1 (𝜑 → (𝜓𝜒))
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:  reu6  2919  f1ocnv2d  6050  nnoddn2prm  12201
  Copyright terms: Public domain W3C validator