Theorem luklem1 938

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-1 935	. . 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 939  luklem3 940  luklem4 941  luklem5 942  luklem6 943  luklem7 944  ax2 947  ax3 948

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

Copyright terms: Public domain