Theorem import-L2.1a 91

Description: Importation Lemma.

Assertion

Ref	Expression
import-L2.1a	⊢ ((𝜑 → (𝜓 → 𝜒)) → (¬ (𝜑 → ¬ 𝜓) → 𝜒))

Proof of Theorem import-L2.1a

Step	Hyp	Ref	Expression
1		trnsp-P1.15c 80	. . . . 5 ⊢ ((𝜓 → 𝜒) → (¬ 𝜒 → ¬ 𝜓))
2	1	axL1.SH 30	. . . 4 ⊢ (𝜑 → ((𝜓 → 𝜒) → (¬ 𝜒 → ¬ 𝜓)))
3	2	axL2.SH 31	. . 3 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (¬ 𝜒 → ¬ 𝜓)))
4	3	imcomm-P1.6.AC.SH 50	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (¬ 𝜒 → (𝜑 → ¬ 𝜓)))
5	4	trnsp-P1.15b.AC.SH 79	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:  import-L2.1a.SH  92