Theorem loowoz 67

Description: An alternate for the Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz, due to Barbara Wozniakowska, Reports on Mathematical Logic 10, 129-137 (1978). (Contributed by Mel L. O'Cat, 8-Aug-04.)

Assertion

Ref	Expression
loowoz	⊢ (((φ → ψ) → (φ → χ)) → ((ψ → φ) → (ψ → χ)))

Proof of Theorem loowoz

Step	Hyp	Ref	Expression
1		ax-1 3	. . 3 ⊢ (ψ → (φ → ψ))
2	1	syl4 19	. 2 ⊢ (((φ → ψ) → (φ → χ)) → (ψ → (φ → χ)))
3	2	a2d 15	1 ⊢ (((φ → ψ) → (φ → χ)) → ((ψ → φ) → (ψ → χ)))

Syntax hints:   → wi 2

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

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