Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxp 4539 | . . . 4 | |
2 | df-br 3900 | . . . . 5 | |
3 | vex 2663 | . . . . . 6 | |
4 | vex 2663 | . . . . . 6 | |
5 | brcodir 4896 | . . . . . 6 | |
6 | 3, 4, 5 | mp2an 422 | . . . . 5 |
7 | 2, 6 | bitr3i 185 | . . . 4 |
8 | 1, 7 | imbi12i 238 | . . 3 |
9 | 8 | 2albii 1432 | . 2 |
10 | relxp 4618 | . . 3 | |
11 | ssrel 4597 | . . 3 | |
12 | 10, 11 | ax-mp 5 | . 2 |
13 | r2al 2431 | . 2 | |
14 | 9, 12, 13 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wex 1453 wcel 1465 wral 2393 cvv 2660 wss 3041 cop 3500 class class class wbr 3899 cxp 4507 ccnv 4508 ccom 4513 wrel 4514 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |