Theorem luklem2 1424

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

Proof of Theorem luklem2

Step	Hyp	Ref	Expression
1		luk-1 1420	. . 3 |- ((ph -> -. ps) -> ((-. ps -> ch) -> (ph -> ch)))
2		luk-3 1422	. . . 4 |- (ps -> (-. ps -> ch))
3		luk-1 1420	. . . 4 |- ((ps -> (-. ps -> ch)) -> (((-. ps -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch))))
4	2, 3	ax-mp 5	. . 3 |- (((-. ps -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch)))
5	1, 4	luklem1 1423	. 2 |- ((ph -> -. ps) -> (ps -> (ph -> ch)))
6		luk-1 1420	. 2 |- ((ps -> (ph -> ch)) -> (((ph -> ch) -> th) -> (ps -> th)))
7	5, 6	luklem1 1423	1 |- ((ph -> -. ps) -> (((ph -> ch) -> th) -> (ps -> th)))

Syntax hints:  -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-meredith 1406

This theorem is referenced by:  luklem3  1425  luklem6  1428  ax3  1433