Theorem loolin 173

Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. For a version not using ax-3 8, see loolinALT 95. (Contributed by O'Cat, 12-Aug-2004.) (Proof shortened by Wolf Lammen, 2-Nov-2012.)

Assertion

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

Proof of Theorem loolin

Step	Hyp	Ref	Expression
1		pm2.521 146	. 2 ⊢ (¬ (φ → ψ) → (ψ → φ))
2		id 19	. 2 ⊢ ((ψ → φ) → (ψ → φ))
3	1, 2	ja 153	1 ⊢ (((φ → ψ) → (ψ → φ)) → (ψ → φ))

Syntax hints:   → 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)