merco1lem18 - Metamath Proof Explorer

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Theorem merco1lem18 1659

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1638. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

**Assertion**
Ref	Expression
merco1lem18

**Proof of Theorem merco1lem18**
Step	Hyp	Ref	Expression
1		merco1 1638	. . . 4
2		merco1lem17 1658	. . . 4
3	1, 2	ax-mp 5	. . 3
4		merco1lem17 1658	. . 3
5	3, 4	ax-mp 5	. 2
6		merco1lem5 1645	. . . . . . 7
7		merco1lem3 1643	. . . . . . 7
8	6, 7	ax-mp 5	. . . . . 6
9		merco1lem5 1645	. . . . . 6
10	8, 9	ax-mp 5	. . . . 5
11		merco1lem4 1644	. . . . 5
12	10, 11	ax-mp 5	. . . 4
13		merco1 1638	. . . . 5
14		merco1lem2 1642	. . . . 5
15	13, 14	ax-mp 5	. . . 4
16	12, 15	ax-mp 5	. . 3
17		merco1lem9 1650	. . 3
18	16, 17	ax-mp 5	. 2
19	5, 18	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: retbwax1 1660

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