Theorem luklem2 662

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

Assertion

Ref	Expression
luklem2	|- ((ph -> -. ps) -> (((ph -> ch) -> th) -> (ps -> th)))

Proof of Theorem luklem2

Step	Hyp	Ref	Expression
1		luk-1 658	. . 3 |- ((ph -> -. ps) -> ((-. ps -> ch) -> (ph -> ch)))
2		luk-3 660	. . . 4 |- (ps -> (-. ps -> ch))
3		luk-1 658	. . . 4 |- ((ps -> (-. ps -> ch)) -> (((-. ps -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch))))
4	2, 3	ax-mp 6	. . 3 |- (((-. ps -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch)))
5	1, 4	luklem1 661	. 2 |- ((ph -> -. ps) -> (ps -> (ph -> ch)))
6		luk-1 658	. 2 |- ((ps -> (ph -> ch)) -> (((ph -> ch) -> th) -> (ps -> th)))
7	5, 6	luklem1 661	1 |- ((ph -> -. ps) -> (((ph -> ch) -> th) -> (ps -> th)))

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  luklem3 663  luklem6 666  ax3 671

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

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