Theorem luklem8 1430

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 1420	. 2 ⊢ ((χ → φ) → ((φ → ψ) → (χ → ψ)))
2		luklem7 1429	. 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-meredith 1406

This theorem is referenced by:  ax2  1432