Theorem expt 177

Description: Exportation theorem pm3.3 448 (closed form of ex 412) expressed with primitive connectives. (Contributed by NM, 28-Dec-1992.)

Assertion

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

Proof of Theorem expt

Step	Hyp	Ref	Expression
1		pm3.2im 160	. . 3 ⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))
2	1	imim1d 82	. 2 ⊢ (𝜑 → ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜓 → 𝜒)))
3	2	com12 32	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)