Theorem export-L2.1b 93

Description: Exportation Lemma.

Assertion

Ref	Expression
export-L2.1b	⊢ ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜑 → (𝜓 → 𝜒)))

Proof of Theorem export-L2.1b

Step	Hyp	Ref	Expression
1		trnsp-P1.15b 78	. . 3 ⊢ ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (¬ 𝜒 → (𝜑 → ¬ 𝜓)))
2	1	imcomm-P1.6.AC.SH 50	. 2 ⊢ ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜑 → (¬ 𝜒 → ¬ 𝜓)))
3	2	trnsp-P1.15d.2AC.SH 85	1 ⊢ ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜑 → (𝜓 → 𝜒)))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem is referenced by:  export-L2.1b.SH  94