Theorem merco1lem17 1566

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1546. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merco1lem17

Proof of Theorem merco1lem17

Step	Hyp	Ref	Expression
1		merco1lem11 1560	. . . . . 6
2		merco1lem7 1555	. . . . . . . 8
3		merco1 1546	. . . . . . . 8
4	2, 3	ax-mp 5	. . . . . . 7
5		merco1lem9 1558	. . . . . . 7
6	4, 5	ax-mp 5	. . . . . 6
7	1, 6	ax-mp 5	. . . . 5
8		merco1 1546	. . . . 5
9	7, 8	ax-mp 5	. . . 4
10		merco1lem11 1560	. . . . . 6
11		merco1lem7 1555	. . . . . . . 8
12		merco1 1546	. . . . . . . 8
13	11, 12	ax-mp 5	. . . . . . 7
14		merco1lem9 1558	. . . . . . 7
15	13, 14	ax-mp 5	. . . . . 6
16	10, 15	ax-mp 5	. . . . 5
17		merco1 1546	. . . . 5
18	16, 17	ax-mp 5	. . . 4
19	9, 18	ax-mp 5	. . 3
20		merco1lem4 1552	. . 3
21		merco1lem16 1565	. . 3
22	19, 20, 21	mpsyl 63	. 2
23		merco1 1546	. 2
24	22, 23	ax-mp 5	1

Syntax hints:  ->wi 4  wfal 1400

This theorem is referenced by:  merco1lem18  1567

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