Theorem luklem5 1666

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
luklem5	⊢ (𝜑 → (𝜓 → 𝜑))

Proof of Theorem luklem5

Step	Hyp	Ref	Expression
1		luklem3 1664	. 2 ⊢ (𝜑 → (((¬ 𝜑 → 𝜑) → 𝜑) → (𝜓 → 𝜑)))
2		luklem4 1665	. 2 ⊢ ((((¬ 𝜑 → 𝜑) → 𝜑) → (𝜓 → 𝜑)) → (𝜓 → 𝜑))
3	1, 2	luklem1 1662	1 ⊢ (𝜑 → (𝜓 → 𝜑))

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:  luklem6  1667  luklem7  1668  ax1  1670