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Mirrors > Home > MPE Home > Th. List > swoord2 | Unicode version |
Description: The incomparability equivalence relation is compatible with the original order. (Contributed by Mario Carneiro, 31-Dec-2014.) |
Ref | Expression |
---|---|
swoer.1 |
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swoer.2 |
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swoer.3 |
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swoord.4 |
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swoord.5 |
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swoord.6 |
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Ref | Expression |
---|---|
swoord2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 20 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() | |
2 | swoord.5 |
. . . 4
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3 | swoord.6 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | swoer.1 |
. . . . . . 7
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5 | difss 3434 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 4, 5 | eqsstri 3338 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 6 | ssbri 4214 |
. . . . 5
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8 | df-br 4173 |
. . . . . 6
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9 | opelxp1 4870 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 8, 9 | sylbi 188 |
. . . . 5
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11 | 3, 7, 10 | 3syl 19 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | swoord.4 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | swoer.3 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 13 | swopolem 4472 |
. . . 4
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15 | 1, 2, 11, 12, 14 | syl13anc 1186 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | idd 22 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 4 | brdifun 6891 |
. . . . . . . 8
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18 | 11, 12, 17 | syl2anc 643 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 3, 18 | mpbid 202 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | olc 374 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 19, 20 | nsyl 115 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21 | pm2.21d 100 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 16, 22 | jaod 370 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 15, 23 | syld 42 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 13 | swopolem 4472 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 1, 2, 12, 11, 25 | syl13anc 1186 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | idd 22 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
28 | orc 375 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 19, 28 | nsyl 115 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 29 | pm2.21d 100 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 27, 30 | jaod 370 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 26, 31 | syld 42 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 24, 32 | impbid 184 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2385 ax-sep 4290 ax-nul 4298 ax-pr 4363 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2258 df-mo 2259 df-clab 2391 df-cleq 2397 df-clel 2400 df-nfc 2529 df-ne 2569 df-ral 2671 df-rex 2672 df-rab 2675 df-v 2918 df-dif 3283 df-un 3285 df-in 3287 df-ss 3294 df-nul 3589 df-if 3700 df-sn 3780 df-pr 3781 df-op 3783 df-br 4173 df-opab 4227 df-xp 4843 df-cnv 4845 |
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