Theorem simprim 166

Description: Simplification. Similar to Theorem *3.27 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)

Assertion

Ref	Expression
simprim	⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜓)

Proof of Theorem simprim

Step	Hyp	Ref	Expression
1		idd 24	. 2 ⊢ (𝜑 → (𝜓 → 𝜓))
2	1	impi 164	1 ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  impt  178  impbi  207  biimpr  219  imbi12  346