Theorem mercolem4 1573

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco2 1569. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
mercolem4

Proof of Theorem mercolem4

Step	Hyp	Ref	Expression
1		merco2 1569	. 2
2		merco2 1569	. . . 4
3		merco2 1569	. . . . . . . . 9
4		mercolem1 1570	. . . . . . . . 9
5	3, 4	ax-mp 5	. . . . . . . 8
6		mercolem1 1570	. . . . . . . 8
7	5, 6	ax-mp 5	. . . . . . 7
8		merco2 1569	. . . . . . 7
9	7, 8	ax-mp 5	. . . . . 6
10		mercolem3 1572	. . . . . 6
11	9, 10	ax-mp 5	. . . . 5
12		merco2 1569	. . . . 5
13	11, 12	ax-mp 5	. . . 4
14	2, 13	ax-mp 5	. . 3
15	1, 14	ax-mp 5	. 2
16	1, 15	ax-mp 5	1

Syntax hints:  ->wi 4  wfal 1400

This theorem is referenced by:  mercolem6  1575  mercolem7  1576

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