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Theorem pm2.1dc 744
Description: Commuted law of the excluded middle for a decidable proposition. Based on theorem *2.1 of [WhiteheadRussell] p. 101. (Contributed by Jim Kingdon, 25-Mar-2018.)
Assertion
Ref Expression
pm2.1dc (DECID φ → (¬ φ φ))

Proof of Theorem pm2.1dc
StepHypRef Expression
1 df-dc 742 . . 3 (DECID φ ↔ (φ ¬ φ))
2 orcom 646 . . 3 ((φ ¬ φ) ↔ (¬ φ φ))
31, 2bitri 173 . 2 (DECID φ ↔ (¬ φ φ))
43biimpi 113 1 (DECID φ → (¬ φ φ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 628  DECID wdc 741
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-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  pm2.6dc  758  rabrsndc  3429
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