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Theorem pm4.67dc 855
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) ↔ (¬ 𝜑𝜓))))

Proof of Theorem pm4.67dc
StepHypRef Expression
1 dcn 810 . 2 (DECID 𝜑DECID ¬ 𝜑)
2 pm4.63dc 854 . 2 (DECID ¬ 𝜑 → (DECID 𝜓 → (¬ (¬ 𝜑 → ¬ 𝜓) ↔ (¬ 𝜑𝜓))))
31, 2syl 14 1 (DECID 𝜑 → (DECID 𝜓 → (¬ (¬ 𝜑 → ¬ 𝜓) ↔ (¬ 𝜑𝜓))))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 103  wb 104  DECID wdc 802
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-stab 799  df-dc 803
This theorem is referenced by: (None)
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