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Theorem pm4.63dc 779
 Description: Theorem *4.63 of [WhiteheadRussell] p. 120, for decidable propositions. (Contributed by Jim Kingdon, 1-May-2018.)
Assertion
Ref Expression
pm4.63dc (DECID φ → (DECID ψ → (¬ (φ → ¬ ψ) ↔ (φ ψ))))

Proof of Theorem pm4.63dc
StepHypRef Expression
1 dfandc 777 . . . 4 (DECID φ → (DECID ψ → ((φ ψ) ↔ ¬ (φ → ¬ ψ))))
21imp 115 . . 3 ((DECID φ DECID ψ) → ((φ ψ) ↔ ¬ (φ → ¬ ψ)))
32bicomd 129 . 2 ((DECID φ DECID ψ) → (¬ (φ → ¬ ψ) ↔ (φ ψ)))
43ex 108 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 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-in1 544  ax-in2 545  ax-io 629 This theorem depends on definitions:  df-bi 110  df-dc 742 This theorem is referenced by:  pm4.67dc  780
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