mercolem5 - Metamath Proof Explorer

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Theorem mercolem5 1666

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
mercolem5

**Proof of Theorem mercolem5**
Step	Hyp	Ref	Expression
1		merco2 1661	. 2
2		merco2 1661	. . . . 5
3		mercolem1 1662	. . . . 5
4	2, 3	ax-mp 5	. . . 4
5		mercolem2 1663	. . . . 5
6		merco2 1661	. . . . 5
7	5, 6	ax-mp 5	. . . 4
8	4, 7	ax-mp 5	. . 3
9	1, 8	ax-mp 5	. 2
10	1, 9	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: mercolem6 1667 mercolem7 1668

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