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Theorem mercolem6 1507
 Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco2 1501. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
mercolem6

Proof of Theorem mercolem6
StepHypRef Expression
1 merco2 1501 . 2
2 mercolem1 1502 . . . . . . . 8
3 mercolem1 1502 . . . . . . . 8
42, 3ax-mp 5 . . . . . . 7
5 mercolem5 1506 . . . . . . . 8
6 mercolem4 1505 . . . . . . . 8
75, 6ax-mp 5 . . . . . . 7
84, 7ax-mp 5 . . . . . 6
91, 8ax-mp 5 . . . . 5
10 mercolem1 1502 . . . . . . . 8
11 mercolem1 1502 . . . . . . . 8
1210, 11ax-mp 5 . . . . . . 7
13 mercolem5 1506 . . . . . . . 8
14 mercolem4 1505 . . . . . . . 8
1513, 14ax-mp 5 . . . . . . 7
1612, 15ax-mp 5 . . . . . 6
171, 16ax-mp 5 . . . . 5
189, 17ax-mp 5 . . . 4
191, 18ax-mp 5 . . 3
201, 19ax-mp 5 . 2
211, 20ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wfal 1317 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 177  df-tru 1319  df-fal 1320 This theorem is referenced by:  mercolem7  1508  re1tbw1  1510  re1tbw2  1511  re1tbw3  1512
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