Theorem luklem3 1425

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 1422	. 2 ⊢ (φ → (¬ φ → ¬ θ))
2		luklem2 1424	. 2 ⊢ ((¬ φ → ¬ θ) → (((¬ φ → ψ) → χ) → (θ → χ)))
3	1, 2	luklem1 1423	1 ⊢ (φ → (((¬ φ → ψ) → χ) → (θ → χ)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-meredith 1406

This theorem is used by:  luklem4  1426  luklem5  1427