Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  mercolem8 Structured version   Unicode version

Theorem mercolem8 1518
 Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco2 1510. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
mercolem8

Proof of Theorem mercolem8
StepHypRef Expression
1 merco2 1510 . 2
2 merco2 1510 . . . . 5
3 mercolem3 1513 . . . . 5
42, 3ax-mp 8 . . . 4
5 mercolem7 1517 . . . . . 6
6 mercolem7 1517 . . . . . 6
75, 6ax-mp 8 . . . . 5
8 merco2 1510 . . . . 5
97, 8ax-mp 8 . . . 4
104, 9ax-mp 8 . . 3
111, 10ax-mp 8 . 2
121, 11ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wfal 1326 This theorem is referenced by:  re1tbw1  1519 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-tru 1328  df-fal 1329
 Copyright terms: Public domain W3C validator