Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  merco1lem3 Structured version   Unicode version

Theorem merco1lem3 1492
 Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1487. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem3

Proof of Theorem merco1lem3
StepHypRef Expression
1 merco1lem2 1491 . . 3
2 retbwax2 1490 . . . 4
3 merco1lem2 1491 . . . 4
42, 3ax-mp 8 . . 3
51, 4ax-mp 8 . 2
6 merco1lem2 1491 . . 3
7 retbwax2 1490 . . . 4
8 merco1lem2 1491 . . . 4
97, 8ax-mp 8 . . 3
106, 9ax-mp 8 . 2
115, 10ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wfal 1326 This theorem is referenced by:  merco1lem4  1493  merco1lem6  1495  merco1lem11  1501  merco1lem12  1502  merco1lem18  1508 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