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Theorem pm2.53 628
Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 778). (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 pm2.24 539 . 2 (φ → (¬ φψ))
2 ax-1 5 . 2 (ψ → (¬ φψ))
31, 2jaoi 623 1 ((φ ψ) → (¬ φψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 616
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 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  ori  629  ord  630  orel1  631  pm2.63  700  notnot2dc  739  dfordc  779  pm5.6r  822  xorbin  1256  19.33b2  1498  onsucelsucexmid  4195  oprabidlem  5456
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