Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.53 GIF version

Theorem pm2.53 711
 Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 876). (Contributed by NM, 3-Jan-2005.) (Revised by NM, 31-Jan-2015.)
Assertion
Ref Expression
pm2.53 ((𝜑𝜓) → (¬ 𝜑𝜓))

Proof of Theorem pm2.53
StepHypRef Expression
1 pm2.24 610 . 2 (𝜑 → (¬ 𝜑𝜓))
2 ax-1 6 . 2 (𝜓 → (¬ 𝜑𝜓))
31, 2jaoi 705 1 ((𝜑𝜓) → (¬ 𝜑𝜓))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 697 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 604  ax-io 698 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  ori  712  ord  713  orel1  714  pm2.63  789  notnotrdc  828  dfordc  877  pm5.6r  912  xorbin  1362  19.33b2  1608  onsucelsucexmid  4440  oprabidlem  5795  omnimkv  7023  xnn0nnn0pnf  9046  absle  10854
 Copyright terms: Public domain W3C validator