Theorem luklem1 1065

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

Hypotheses

Ref	Expression
luklem1.1	|- (ph -> ps)
luklem1.2	|- (ps -> ch)

Assertion

Ref	Expression
luklem1	|- (ph -> ch)

Proof of Theorem luklem1

Step	Hyp	Ref	Expression
1		luklem1.2	. 2 |- (ps -> ch)
2		luklem1.1	. . 3 |- (ph -> ps)
3		luk-1 1062	. . 3 |- ((ph -> ps) -> ((ps -> ch) -> (ph -> ch)))
4	2, 3	ax-mp 7	. 2 |- ((ps -> ch) -> (ph -> ch))
5	1, 4	ax-mp 7	1 |- (ph -> ch)

Syntax hints:   -> wi 3

This theorem is referenced by:  luklem2 1066  luklem3 1067  luklem4 1068  luklem5 1069  luklem6 1070  luklem7 1071  ax2 1074  ax3 1075

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

This theorem depends on definitions:  df-bi 163  df-an 241

Copyright terms: Public domain