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Mirrors > Home > ILE Home > Th. List > pocl | Unicode version |
Description: Properties of partial order relation in class notation. (Contributed by NM, 27-Mar-1997.) |
Ref | Expression |
---|---|
pocl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. . . . . . 7
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2 | 1, 1 | breq12d 3768 |
. . . . . 6
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3 | 2 | notbid 591 |
. . . . 5
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4 | breq1 3758 |
. . . . . . 7
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5 | 4 | anbi1d 438 |
. . . . . 6
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6 | breq1 3758 |
. . . . . 6
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7 | 5, 6 | imbi12d 223 |
. . . . 5
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8 | 3, 7 | anbi12d 442 |
. . . 4
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9 | 8 | imbi2d 219 |
. . 3
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10 | breq2 3759 |
. . . . . . 7
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11 | breq1 3758 |
. . . . . . 7
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12 | 10, 11 | anbi12d 442 |
. . . . . 6
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13 | 12 | imbi1d 220 |
. . . . 5
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14 | 13 | anbi2d 437 |
. . . 4
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15 | 14 | imbi2d 219 |
. . 3
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16 | breq2 3759 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 16 | anbi2d 437 |
. . . . . 6
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18 | breq2 3759 |
. . . . . 6
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19 | 17, 18 | imbi12d 223 |
. . . . 5
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20 | 19 | anbi2d 437 |
. . . 4
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21 | 20 | imbi2d 219 |
. . 3
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22 | df-po 4024 |
. . . . . . . 8
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23 | r3al 2360 |
. . . . . . . 8
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24 | 22, 23 | bitri 173 |
. . . . . . 7
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25 | 24 | biimpi 113 |
. . . . . 6
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26 | 25 | 19.21bbi 1448 |
. . . . 5
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27 | 26 | 19.21bi 1447 |
. . . 4
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28 | 27 | com12 27 |
. . 3
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29 | 9, 15, 21, 28 | vtocl3ga 2617 |
. 2
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30 | 29 | com12 27 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 df-op 3376 df-br 3756 df-po 4024 |
This theorem is referenced by: poirr 4035 potr 4036 |
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