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Theorem mercolem4 1514
 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
mercolem4

Proof of Theorem mercolem4
StepHypRef Expression
1 merco2 1510 . 2
2 merco2 1510 . . . 4
3 merco2 1510 . . . . . . . . 9
4 mercolem1 1511 . . . . . . . . 9
53, 4ax-mp 8 . . . . . . . 8
6 mercolem1 1511 . . . . . . . 8
75, 6ax-mp 8 . . . . . . 7
8 merco2 1510 . . . . . . 7
97, 8ax-mp 8 . . . . . 6
10 mercolem3 1513 . . . . . 6
119, 10ax-mp 8 . . . . 5
12 merco2 1510 . . . . 5
1311, 12ax-mp 8 . . . 4
142, 13ax-mp 8 . . 3
151, 14ax-mp 8 . 2
161, 15ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wfal 1326 This theorem is referenced by:  mercolem6  1516  mercolem7  1517 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
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