Theorem loowoz 112

Description: An alternate for the Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz loolin 111, due to Barbara Wozniakowska, Reports on Mathematical Logic 10, 129-137 (1978). (Contributed by Mel L. O'Cat, 8-Aug-2004.)

Assertion

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

Proof of Theorem loowoz

Step	Hyp	Ref	Expression
1		jarr 106	. 2 ⊢ (((𝜑 → 𝜓) → (𝜑 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))
2	1	a2d 29	1 ⊢ (((𝜑 → 𝜓) → (𝜑 → 𝜒)) → ((𝜓 → 𝜑) → (𝜓 → 𝜒)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by: (None)