ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anc2li GIF version

Theorem anc2li 327
Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)
Hypothesis
Ref Expression
anc2li.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
anc2li (𝜑 → (𝜓 → (𝜑𝜒)))

Proof of Theorem anc2li
StepHypRef Expression
1 anc2li.1 . 2 (𝜑 → (𝜓𝜒))
2 id 19 . 2 (𝜑𝜑)
31, 2jctild 314 1 (𝜑 → (𝜓 → (𝜑𝜒)))
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:  imdistani  442  equvini  1732  sssnm  3688  tfis  4504  indpi  7173
  Copyright terms: Public domain W3C validator