Theorem luklem8 668

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

Assertion

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

Proof of Theorem luklem8

Step	Hyp	Ref	Expression
1		luk-1 658	. 2 ⊢ ((χ → φ) → ((φ → ψ) → (χ → ψ)))
2		luklem7 667	. 2 ⊢ (((χ → φ) → ((φ → ψ) → (χ → ψ))) → ((φ → ψ) → ((χ → φ) → (χ → ψ))))
3	1, 2	ax-mp 6	1 ⊢ ((φ → ψ) → ((χ → φ) → (χ → ψ)))

Syntax hints:   → wi 2

This theorem is referenced by:  ax2 670

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

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