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Theorem pm4.67dc 774
Description: Theorem *4.67 of [WhiteheadRussell] p. 120, for decidable propositions. (Contributed by Jim Kingdon, 1-May-2018.)
Assertion
Ref Expression
pm4.67dc (DECID φ → (DECID ψ → (¬ (¬ φ → ¬ ψ) ↔ (¬ φ ψ))))

Proof of Theorem pm4.67dc
StepHypRef Expression
1 dcn 737 . 2 (DECID φDECID ¬ φ)
2 pm4.63dc 773 . 2 (DECID ¬ φ → (DECID ψ → (¬ (¬ φ → ¬ ψ) ↔ (¬ φ ψ))))
31, 2syl 14 1 (DECID φ → (DECID ψ → (¬ (¬ φ → ¬ ψ) ↔ (¬ φ ψ))))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97  wb 98  DECID wdc 733
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-in1 532  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110  df-dc 734
This theorem is referenced by: (None)
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