Theorem loolin 66

Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. (Contributed by Mel L. O'Cat, 12-Aug-04.)

Assertion

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

Proof of Theorem loolin

Step	Hyp	Ref	Expression
1		ax-1 3	. . 3 ⊢ (ψ → (φ → ψ))
2	1	syl4 19	. 2 ⊢ (((φ → ψ) → (ψ → φ)) → (ψ → (ψ → φ)))
3	2	pm2.43d 59	1 ⊢ (((φ → ψ) → (ψ → φ)) → (ψ → φ))

Syntax hints:   → wi 2

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6

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