Theorem luklem3 1663

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
luklem3	⊢ (𝜑 → (((¬ 𝜑 → 𝜓) → 𝜒) → (𝜃 → 𝜒)))

Proof of Theorem luklem3

Step	Hyp	Ref	Expression
1		luk-3 1660	. 2 ⊢ (𝜑 → (¬ 𝜑 → ¬ 𝜃))
2		luklem2 1662	. 2 ⊢ ((¬ 𝜑 → ¬ 𝜃) → (((¬ 𝜑 → 𝜓) → 𝜒) → (𝜃 → 𝜒)))
3	1, 2	luklem1 1661	1 ⊢ (𝜑 → (((¬ 𝜑 → 𝜓) → 𝜒) → (𝜃 → 𝜒)))

Syntax hints:  ¬ wn 3   → 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:  luklem4  1664  luklem5  1665