ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.21ni GIF version

Theorem pm5.21ni 652
Description: Two propositions implying a false one are equivalent. (Contributed by NM, 16-Feb-1996.) (Proof shortened by Wolf Lammen, 19-May-2013.)
Hypotheses
Ref Expression
pm5.21ni.1 (𝜑𝜓)
pm5.21ni.2 (𝜒𝜓)
Assertion
Ref Expression
pm5.21ni 𝜓 → (𝜑𝜒))

Proof of Theorem pm5.21ni
StepHypRef Expression
1 pm5.21ni.1 . . 3 (𝜑𝜓)
21con3i 595 . 2 𝜓 → ¬ 𝜑)
3 pm5.21ni.2 . . 3 (𝜒𝜓)
43con3i 595 . 2 𝜓 → ¬ 𝜒)
52, 42falsed 651 1 𝜓 → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  niabn  909
  Copyright terms: Public domain W3C validator