Theorem simprimdc 860

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

Step	Hyp	Ref	Expression
1		idd 21	. . 3 ⊢ (𝜑 → (𝜓 → 𝜓))
2	1	a1i 9	. 2 ⊢ (DECID 𝜓 → (𝜑 → (𝜓 → 𝜓)))
3	2	impidc 859	1 ⊢ (DECID 𝜓 → (¬ (𝜑 → ¬ 𝜓) → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4  DECID wdc 835

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710

This theorem depends on definitions:  df-bi 117  df-stab 832  df-dc 836

This theorem is referenced by:  dfandc  885