Theorem merco1lem11 1560

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
merco1lem11

Proof of Theorem merco1lem11

Step	Hyp	Ref	Expression
1		merco1lem5 1553	. . . . . 6
2		merco1lem3 1551	. . . . . 6
3	1, 2	ax-mp 5	. . . . 5
4		merco1lem4 1552	. . . . 5
5	3, 4	ax-mp 5	. . . 4
6		merco1lem5 1553	. . . 4
7	5, 6	ax-mp 5	. . 3
8		merco1lem4 1552	. . 3
9	7, 8	ax-mp 5	. 2
10		merco1 1546	. . 3
11		merco1lem2 1550	. . 3
12	10, 11	ax-mp 5	. 2
13	9, 12	ax-mp 5	1

Syntax hints:  ->wi 4  wfal 1400

This theorem is referenced by:  merco1lem12  1561  merco1lem16  1565  merco1lem17  1566

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