Theorem mercolem5 1574

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco2 1569. (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 1569	. 2
2		merco2 1569	. . . . 5
3		mercolem1 1570	. . . . 5
4	2, 3	ax-mp 5	. . . 4
5		mercolem2 1571	. . . . 5
6		merco2 1569	. . . . 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

Syntax hints:  ->wi 4  wfal 1400

This theorem is referenced by:  mercolem6  1575  mercolem7  1576

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