Theorem luklem1 1583

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 23-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

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 1580	. . 3 |- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )
4	2, 3	ax-mp 5	. 2 |- ( ( ps -> ch ) -> ( ph -> ch ) )
5	1, 4	ax-mp 5	1 |- ( ph -> ch )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  luklem2  1584  luklem3  1585  luklem4  1586  luklem5  1587  luklem6  1588  luklem7  1589  ax2  1592  ax3  1593