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Theorem mercolem4 1573
 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
mercolem4

Proof of Theorem mercolem4
StepHypRef Expression
1 merco2 1569 . 2
2 merco2 1569 . . . 4
3 merco2 1569 . . . . . . . . 9
4 mercolem1 1570 . . . . . . . . 9
53, 4ax-mp 5 . . . . . . . 8
6 mercolem1 1570 . . . . . . . 8
75, 6ax-mp 5 . . . . . . 7
8 merco2 1569 . . . . . . 7
97, 8ax-mp 5 . . . . . 6
10 mercolem3 1572 . . . . . 6
119, 10ax-mp 5 . . . . 5
12 merco2 1569 . . . . 5
1311, 12ax-mp 5 . . . 4
142, 13ax-mp 5 . . 3
151, 14ax-mp 5 . 2
161, 15ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4   wfal 1400 This theorem is referenced by:  mercolem6  1575  mercolem7  1576 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
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