Theorem luklem3 663

Description: Lemma for rederiving standard propositional axioms from Lukasiewicz'.

Assertion

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

Proof of Theorem luklem3

Step	Hyp	Ref	Expression
1		luk-3 660	. 2 ⊢ (φ → (¬ φ → ¬ θ))
2		luklem2 662	. 2 ⊢ ((¬ φ → ¬ θ) → (((¬ φ → ψ) → χ) → (θ → χ)))
3	1, 2	luklem1 661	1 ⊢ (φ → (((¬ φ → ψ) → χ) → (θ → χ)))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  luklem4 664  luklem5 665

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

metamath.org