Theorem luklem7 1429

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
luklem7	|- ((ph -> (ps -> ch)) -> (ps -> (ph -> ch)))

Proof of Theorem luklem7

Step	Hyp	Ref	Expression
1		luk-1 1420	. 2 |- ((ph -> (ps -> ch)) -> (((ps -> ch) -> ch) -> (ph -> ch)))
2		luklem5 1427	. . . . 5 |- (ps -> ((ps -> ch) -> ps))
3		luk-1 1420	. . . . 5 |- (((ps -> ch) -> ps) -> ((ps -> ch) -> ((ps -> ch) -> ch)))
4	2, 3	luklem1 1423	. . . 4 |- (ps -> ((ps -> ch) -> ((ps -> ch) -> ch)))
5		luklem6 1428	. . . 4 |- (((ps -> ch) -> ((ps -> ch) -> ch)) -> ((ps -> ch) -> ch))
6	4, 5	luklem1 1423	. . 3 |- (ps -> ((ps -> ch) -> ch))
7		luk-1 1420	. . 3 |- ((ps -> ((ps -> ch) -> ch)) -> ((((ps -> ch) -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch))))
8	6, 7	ax-mp 5	. 2 |- ((((ps -> ch) -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch)))
9	1, 8	luklem1 1423	1 |- ((ph -> (ps -> ch)) -> (ps -> (ph -> ch)))

Syntax hints:   -> wi 4

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

This theorem is referenced by:  luklem8  1430  ax2  1432