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Theorem simprimdc 845
Description: Simplification given a decidable proposition. Similar to Theorem *3.27 (Simp) of [WhiteheadRussell] p. 112. (Contributed by Jim Kingdon, 30-Apr-2018.)
Assertion
Ref Expression
simprimdc (DECID 𝜓 → (¬ (𝜑 → ¬ 𝜓) → 𝜓))

Proof of Theorem simprimdc
StepHypRef Expression
1 idd 21 . . 3 (𝜑 → (𝜓𝜓))
21a1i 9 . 2 (DECID 𝜓 → (𝜑 → (𝜓𝜓)))
32impidc 844 1 (DECID 𝜓 → (¬ (𝜑 → ¬ 𝜓) → 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  DECID wdc 820
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 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821
This theorem is referenced by:  dfandc  870
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