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Theorem pm2.53 640
 Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 789). (Contributed by NM, 3-Jan-2005.) (Revised by NM, 31-Jan-2015.)
Assertion
Ref Expression
pm2.53 ((φ ψ) → (¬ φψ))

Proof of Theorem pm2.53
StepHypRef Expression
1 pm2.24 551 . 2 (φ → (¬ φψ))
2 ax-1 5 . 2 (ψ → (¬ φψ))
31, 2jaoi 635 1 ((φ ψ) → (¬ φψ))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 628 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 629 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  ori  641  ord  642  orel1  643  pm2.63  712  notnot2dc  750  dfordc  790  pm5.6r  835  xorbin  1272  19.33b2  1517  onsucelsucexmid  4215  oprabidlem  5479
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