Theorem luklem8 1581

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
luklem8	⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Proof of Theorem luklem8

Step	Hyp	Ref	Expression
1		luk-1 1571	. 2 ⊢ ((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓)))
2		luklem7 1580	. 2 ⊢ (((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓))) → ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Syntax hints:   → 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:  ax2  1583