Theorem impt 178

Description: Importation theorem pm3.1 993 (closed form of imp 406) expressed with primitive connectives. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 20-Jul-2013.)

Assertion

Ref	Expression
impt	⊢ ((𝜑 → (𝜓 → 𝜒)) → (¬ (𝜑 → ¬ 𝜓) → 𝜒))

Proof of Theorem impt

Step	Hyp	Ref	Expression
1		simprim 166	. 2 ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜓)
2		simplim 167	. . 3 ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜑)
3	2	imim1i 63	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (¬ (𝜑 → ¬ 𝜓) → (𝜓 → 𝜒)))
4	1, 3	mpdi 45	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (¬ (𝜑 → ¬ 𝜓) → 𝜒))

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: (None)