Theorem loolin 112

Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. See loowoz 113 for an alternate axiom. (Contributed by Mel L. O'Cat, 12-Aug-2004.)

Assertion

Ref	Expression
loolin	⊢ (((𝜑 → 𝜓) → (𝜓 → 𝜑)) → (𝜓 → 𝜑))

Proof of Theorem loolin

Step	Hyp	Ref	Expression
1		jarr 107	. 2 ⊢ (((𝜑 → 𝜓) → (𝜓 → 𝜑)) → (𝜓 → (𝜓 → 𝜑)))
2	1	pm2.43d 54	1 ⊢ (((𝜑 → 𝜓) → (𝜓 → 𝜑)) → (𝜓 → 𝜑))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by: (None)