Theorem tbwlem5 1542

Description: Used to rederive the Lukasiewicz axioms from Tarski-Bernays-Wajsberg'. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
tbwlem5

Proof of Theorem tbwlem5

Step	Hyp	Ref	Expression
1		tbw-ax2 1534	. . . 4
2		tbw-ax1 1533	. . . 4
3	1, 2	tbwsyl 1537	. . 3
4		tbwlem1 1538	. . 3
5	3, 4	ax-mp 5	. 2
6		tbwlem4 1541	. 2
7	5, 6	ax-mp 5	1

Syntax hints:  ->wi 4  wfal 1400

This theorem is referenced by:  re1luk3  1545

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

This theorem depends on definitions:  df-bi 185  df-tru 1398  df-fal 1401