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Theorem merco1lem18 1567
 Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1546. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem18

Proof of Theorem merco1lem18
StepHypRef Expression
1 merco1 1546 . . . 4
2 merco1lem17 1566 . . . 4
31, 2ax-mp 5 . . 3
4 merco1lem17 1566 . . 3
53, 4ax-mp 5 . 2
6 merco1lem5 1553 . . . . . . 7
7 merco1lem3 1551 . . . . . . 7
86, 7ax-mp 5 . . . . . 6
9 merco1lem5 1553 . . . . . 6
108, 9ax-mp 5 . . . . 5
11 merco1lem4 1552 . . . . 5
1210, 11ax-mp 5 . . . 4
13 merco1 1546 . . . . 5
14 merco1lem2 1550 . . . . 5
1513, 14ax-mp 5 . . . 4
1612, 15ax-mp 5 . . 3
17 merco1lem9 1558 . . 3
1816, 17ax-mp 5 . 2
195, 18ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4   wfal 1400 This theorem is referenced by:  retbwax1  1568 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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