ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  con1biddc GIF version

Theorem con1biddc 808
Description: A contraposition deduction. (Contributed by Jim Kingdon, 4-Apr-2018.)
Hypothesis
Ref Expression
con1biddc.1 (𝜑 → (DECID 𝜓 → (¬ 𝜓𝜒)))
Assertion
Ref Expression
con1biddc (𝜑 → (DECID 𝜓 → (¬ 𝜒𝜓)))

Proof of Theorem con1biddc
StepHypRef Expression
1 con1biddc.1 . 2 (𝜑 → (DECID 𝜓 → (¬ 𝜓𝜒)))
2 con1biimdc 805 . 2 (DECID 𝜓 → ((¬ 𝜓𝜒) → (¬ 𝜒𝜓)))
31, 2sylcom 28 1 (𝜑 → (DECID 𝜓 → (¬ 𝜒𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 103  DECID wdc 780
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-dc 781
This theorem is referenced by:  con2biddc  812  pm5.18dc  815  necon1abiddc  2317  necon1bbiddc  2318
  Copyright terms: Public domain W3C validator