Theorem luklem7 945

Description: Used to rederive standard propositional axioms from Lukasiewicz'.

Assertion

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

Proof of Theorem luklem7

Step	Hyp	Ref	Expression
1		luk-1 936	. 2 |- ((ph -> (ps -> ch)) -> (((ps -> ch) -> ch) -> (ph -> ch)))
2		luklem5 943	. . . . 5 |- (ps -> ((ps -> ch) -> ps))
3		luk-1 936	. . . . 5 |- (((ps -> ch) -> ps) -> ((ps -> ch) -> ((ps -> ch) -> ch)))
4	2, 3	luklem1 939	. . . 4 |- (ps -> ((ps -> ch) -> ((ps -> ch) -> ch)))
5		luklem6 944	. . . 4 |- (((ps -> ch) -> ((ps -> ch) -> ch)) -> ((ps -> ch) -> ch))
6	4, 5	luklem1 939	. . 3 |- (ps -> ((ps -> ch) -> ch))
7		luk-1 936	. . 3 |- ((ps -> ((ps -> ch) -> ch)) -> ((((ps -> ch) -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch))))
8	6, 7	ax-mp 7	. 2 |- ((((ps -> ch) -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch)))
9	1, 8	luklem1 939	1 |- ((ph -> (ps -> ch)) -> (ps -> (ph -> ch)))

Syntax hints:   -> wi 3

This theorem is referenced by:  luklem8 946  ax2 948

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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