Theorem mercolem7 1576

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
mercolem7

Proof of Theorem mercolem7

Step	Hyp	Ref	Expression
1		merco2 1569	. 2
2		mercolem3 1572	. . . 4
3		mercolem6 1575	. . . 4
4	2, 3	ax-mp 5	. . 3
5		mercolem5 1574	. . . 4
6		mercolem4 1573	. . . 4
7	5, 6	ax-mp 5	. . 3
8	4, 7	ax-mp 5	. 2
9	1, 8	ax-mp 5	1

Syntax hints:  ->wi 4  wfal 1400

This theorem is referenced by:  mercolem8  1577

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