Theorem luklem8

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	luklem8	|- ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		luk-1	|- ( ( ch -> ph ) -> ( ( ph -> ps ) -> ( ch -> ps ) ) )
2		luklem7	|- ( ( ( ch -> ph ) -> ( ( ph -> ps ) -> ( ch -> ps ) ) ) -> ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) )
3	1 2	ax-mp	|- ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )