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Theorem mercolem6 1667

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco2 1661. (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 1661	. 2
2		mercolem1 1662	. . . . . . . 8
3		mercolem1 1662	. . . . . . . 8
4	2, 3	ax-mp 5	. . . . . . 7
5		mercolem5 1666	. . . . . . . 8
6		mercolem4 1665	. . . . . . . 8
7	5, 6	ax-mp 5	. . . . . . 7
8	4, 7	ax-mp 5	. . . . . 6
9	1, 8	ax-mp 5	. . . . 5
10		mercolem1 1662	. . . . . . . 8
11		mercolem1 1662	. . . . . . . 8
12	10, 11	ax-mp 5	. . . . . . 7
13		mercolem5 1666	. . . . . . . 8
14		mercolem4 1665	. . . . . . . 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

Colors of variables: wff setvar class

Syntax hints:

wi 4

wfal 1488

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 197 df-tru 1486 df-fal 1489

This theorem is referenced by: mercolem7 1668 re1tbw1 1670 re1tbw2 1671 re1tbw3 1672 pm2.43bgbi 38723

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