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Theorem pm2.53 674
Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 824). (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 pm2.24 584 . 2 (𝜑 → (¬ 𝜑𝜓))
2 ax-1 5 . 2 (𝜓 → (¬ 𝜑𝜓))
31, 2jaoi 669 1 ((𝜑𝜓) → (¬ 𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 662
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-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ori  675  ord  676  orel1  677  pm2.63  747  notnotrdc  785  dfordc  825  pm5.6r  870  xorbin  1316  19.33b2  1561  onsucelsucexmid  4308  oprabidlem  5614  xnn0nnn0pnf  8642  absle  10348
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