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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj908 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj69 29812. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj908.1 |
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bnj908.2 |
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bnj908.3 |
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bnj908.4 |
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bnj908.5 |
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bnj908.10 |
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bnj908.11 |
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bnj908.12 |
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bnj908.13 |
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bnj908.14 |
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bnj908.15 |
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bnj908.16 |
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bnj908.17 |
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bnj908.18 |
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bnj908.19 |
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bnj908.20 |
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bnj908.21 |
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bnj908.22 |
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bnj908.23 |
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bnj908.24 |
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bnj908.25 |
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bnj908.26 |
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Ref | Expression |
---|---|
bnj908 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj248 29498 |
. . . . . 6
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2 | bnj908.4 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | bnj908.10 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | bnj908.11 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | bnj908.12 |
. . . . . . . . . . 11
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6 | vex 3047 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() | |
7 | 2, 3, 4, 5, 6 | bnj207 29685 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 7 | biimpi 198 |
. . . . . . . . 9
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9 | euex 2322 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 8, 9 | syl6 34 |
. . . . . . . 8
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11 | 10 | impcom 432 |
. . . . . . 7
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12 | bnj908.17 |
. . . . . . 7
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13 | 11, 12 | bnj1198 29600 |
. . . . . 6
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14 | 1, 13 | bnj832 29561 |
. . . . 5
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15 | bnj645 29553 |
. . . . 5
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16 | 19.41v 1829 |
. . . . 5
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17 | 14, 15, 16 | sylanbrc 669 |
. . . 4
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18 | bnj642 29551 |
. . . 4
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19 | 19.41v 1829 |
. . . 4
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20 | 17, 18, 19 | sylanbrc 669 |
. . 3
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21 | bnj170 29496 |
. . 3
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22 | 20, 21 | bnj1198 29600 |
. 2
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23 | bnj908.18 |
. . . 4
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24 | bnj908.19 |
. . . 4
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25 | bnj908.1 |
. . . . . 6
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26 | 25, 3, 6 | bnj523 29691 |
. . . . 5
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27 | bnj908.2 |
. . . . . 6
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28 | 27, 4, 6 | bnj539 29695 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | bnj908.3 |
. . . . 5
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30 | bnj908.16 |
. . . . 5
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31 | 26, 28, 29, 30, 12, 23 | bnj544 29698 |
. . . 4
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32 | 23, 24, 31 | bnj561 29707 |
. . 3
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33 | bnj908.13 |
. . . . . 6
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34 | 30 | bnj528 29693 |
. . . . . 6
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35 | 25, 33, 34 | bnj609 29721 |
. . . . 5
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36 | 26, 29, 30, 12, 23, 31, 35 | bnj545 29699 |
. . . 4
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37 | 23, 24, 36 | bnj562 29708 |
. . 3
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38 | bnj908.20 |
. . . 4
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39 | bnj908.22 |
. . . 4
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40 | bnj908.23 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
41 | bnj908.24 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
42 | bnj908.25 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
43 | bnj908.26 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
44 | bnj908.21 |
. . . 4
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45 | bnj908.14 |
. . . . 5
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46 | 27, 45, 34 | bnj611 29722 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
47 | 29, 30, 12, 23, 24, 38, 39, 40, 41, 42, 43, 26, 28, 31, 44, 32, 46 | bnj571 29710 |
. . 3
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48 | 32, 37, 47 | 3jca 1187 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
49 | 22, 48 | bnj593 29548 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-8 1888 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-rep 4514 ax-sep 4524 ax-nul 4533 ax-pr 4638 ax-un 6580 ax-reg 8104 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 985 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-reu 2743 df-rab 2745 df-v 3046 df-sbc 3267 df-csb 3363 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-pss 3419 df-nul 3731 df-if 3881 df-pw 3952 df-sn 3968 df-pr 3970 df-tp 3972 df-op 3974 df-uni 4198 df-iun 4279 df-br 4402 df-opab 4461 df-mpt 4462 df-tr 4497 df-eprel 4744 df-id 4748 df-po 4754 df-so 4755 df-fr 4792 df-we 4794 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-rn 4844 df-res 4845 df-ima 4846 df-ord 5425 df-on 5426 df-lim 5427 df-suc 5428 df-iota 5545 df-fun 5583 df-fn 5584 df-f 5585 df-f1 5586 df-fo 5587 df-f1o 5588 df-fv 5589 df-om 6690 df-bnj17 29485 df-bnj14 29487 df-bnj13 29489 df-bnj15 29491 |
This theorem is referenced by: (None) |
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