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Theorem merco1lem17 1566
 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
merco1lem17

Proof of Theorem merco1lem17
StepHypRef Expression
1 merco1lem11 1560 . . . . . 6
2 merco1lem7 1555 . . . . . . . 8
3 merco1 1546 . . . . . . . 8
42, 3ax-mp 5 . . . . . . 7
5 merco1lem9 1558 . . . . . . 7
64, 5ax-mp 5 . . . . . 6
71, 6ax-mp 5 . . . . 5
8 merco1 1546 . . . . 5
97, 8ax-mp 5 . . . 4
10 merco1lem11 1560 . . . . . 6
11 merco1lem7 1555 . . . . . . . 8
12 merco1 1546 . . . . . . . 8
1311, 12ax-mp 5 . . . . . . 7
14 merco1lem9 1558 . . . . . . 7
1513, 14ax-mp 5 . . . . . 6
1610, 15ax-mp 5 . . . . 5
17 merco1 1546 . . . . 5
1816, 17ax-mp 5 . . . 4
199, 18ax-mp 5 . . 3
20 merco1lem4 1552 . . 3
21 merco1lem16 1565 . . 3
2219, 20, 21mpsyl 63 . 2
23 merco1 1546 . 2
2422, 23ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4   wfal 1400 This theorem is referenced by:  merco1lem18  1567 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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