Theorem luklem8 1590

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	|- ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )

Proof of Theorem luklem8

Step	Hyp	Ref	Expression
1		luk-1 1580	. 2 |- ( ( ch -> ph ) -> ( ( ph -> ps ) -> ( ch -> ps ) ) )
2		luklem7 1589	. 2 |- ( ( ( ch -> ph ) -> ( ( ph -> ps ) -> ( ch -> ps ) ) ) -> ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )

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  1592