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Theorem pm3.37dc 788
Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112, given a decidability condition. (Contributed by Jim Kingdon, 24-Apr-2018.)
Assertion
Ref Expression
pm3.37dc (DECID 𝜒 → (((𝜑𝜓) → 𝜒) → ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)))

Proof of Theorem pm3.37dc
StepHypRef Expression
1 pm4.14dc 787 . 2 (DECID 𝜒 → (((𝜑𝜓) → 𝜒) ↔ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)))
21biimpd 132 1 (DECID 𝜒 → (((𝜑𝜓) → 𝜒) → ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 97  DECID wdc 742
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 630
This theorem depends on definitions:  df-bi 110  df-dc 743
This theorem is referenced by: (None)
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