Theorem mercolem6 1575

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
mercolem6

Proof of Theorem mercolem6

Step	Hyp	Ref	Expression
1		merco2 1569	. 2
2		mercolem1 1570	. . . . . . . 8
3		mercolem1 1570	. . . . . . . 8
4	2, 3	ax-mp 5	. . . . . . 7
5		mercolem5 1574	. . . . . . . 8
6		mercolem4 1573	. . . . . . . 8
7	5, 6	ax-mp 5	. . . . . . 7
8	4, 7	ax-mp 5	. . . . . 6
9	1, 8	ax-mp 5	. . . . 5
10		mercolem1 1570	. . . . . . . 8
11		mercolem1 1570	. . . . . . . 8
12	10, 11	ax-mp 5	. . . . . . 7
13		mercolem5 1574	. . . . . . . 8
14		mercolem4 1573	. . . . . . . 8
15	13, 14	ax-mp 5	. . . . . . 7
16	12, 15	ax-mp 5	. . . . . 6
17	1, 16	ax-mp 5	. . . . 5
18	9, 17	ax-mp 5	. . . 4
19	1, 18	ax-mp 5	. . 3
20	1, 19	ax-mp 5	. 2
21	1, 20	ax-mp 5	1

Syntax hints:  ->wi 4  wfal 1400

This theorem is referenced by:  mercolem7  1576  re1tbw1  1578  re1tbw2  1579  re1tbw3  1580  pm2.43bgbi  33287

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