Theorem luklem7 667

Description: Lemma for rederiving 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-1 658	. 2 |- ((ph -> (ps -> ch)) -> (((ps -> ch) -> ch) -> (ph -> ch)))
2		luklem5 665	. . . . 5 |- (ps -> ((ps -> ch) -> ps))
3		luk-1 658	. . . . 5 |- (((ps -> ch) -> ps) -> ((ps -> ch) -> ((ps -> ch) -> ch)))
4	2, 3	luklem1 661	. . . 4 |- (ps -> ((ps -> ch) -> ((ps -> ch) -> ch)))
5		luklem6 666	. . . 4 |- (((ps -> ch) -> ((ps -> ch) -> ch)) -> ((ps -> ch) -> ch))
6	4, 5	luklem1 661	. . 3 |- (ps -> ((ps -> ch) -> ch))
7		luk-1 658	. . 3 |- ((ps -> ((ps -> ch) -> ch)) -> ((((ps -> ch) -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch))))
8	6, 7	ax-mp 6	. 2 |- ((((ps -> ch) -> ch) -> (ph -> ch)) -> (ps -> (ph -> ch)))
9	1, 8	luklem1 661	1 |- ((ph -> (ps -> ch)) -> (ps -> (ph -> ch)))

Syntax hints:   -> wi 2

This theorem is referenced by:  luklem8 668  ax2 670

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

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