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Mirrors > Home > ILE Home > Th. List > codir | Unicode version |
Description: Two ways of saying a relation is directed. (Contributed by Mario Carneiro, 22-Nov-2013.) |
Ref | Expression |
---|---|
codir |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxp 4529 |
. . . 4
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2 | df-br 3896 |
. . . . 5
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3 | vex 2660 |
. . . . . 6
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4 | vex 2660 |
. . . . . 6
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5 | brcodir 4884 |
. . . . . 6
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6 | 3, 4, 5 | mp2an 420 |
. . . . 5
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7 | 2, 6 | bitr3i 185 |
. . . 4
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8 | 1, 7 | imbi12i 238 |
. . 3
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9 | 8 | 2albii 1430 |
. 2
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10 | relxp 4608 |
. . 3
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11 | ssrel 4587 |
. . 3
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12 | 10, 11 | ax-mp 7 |
. 2
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13 | r2al 2428 |
. 2
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14 | 9, 12, 13 | 3bitr4i 211 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ral 2395 df-rex 2396 df-v 2659 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-br 3896 df-opab 3950 df-xp 4505 df-rel 4506 df-cnv 4507 df-co 4508 |
This theorem is referenced by: (None) |
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