Theorem import-L2.1a.SH 92

Description: Inference from import-L2.1a 91.

Hypothesis

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

Assertion

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

Proof of Theorem import-L2.1a.SH

Step	Hyp	Ref	Expression
1		import-L2.1a.SH.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		import-L2.1a 91	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (¬ (𝜑 → ¬ 𝜓) → 𝜒))
3	1, 2	ax-MP 14	1 ⊢ (¬ (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:  simpl-L2.2a  95  simpr-L2.2b  97