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Mirrors > Home > ILE Home > Th. List > rnco | Unicode version |
Description: The range of the composition of two classes. (Contributed by NM, 12-Dec-2006.) |
Ref | Expression |
---|---|
rnco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2663 | . . . . . 6 | |
2 | vex 2663 | . . . . . 6 | |
3 | 1, 2 | brco 4680 | . . . . 5 |
4 | 3 | exbii 1569 | . . . 4 |
5 | excom 1627 | . . . 4 | |
6 | ancom 264 | . . . . . . 7 | |
7 | 19.41v 1858 | . . . . . . 7 | |
8 | vex 2663 | . . . . . . . . 9 | |
9 | 8 | elrn 4752 | . . . . . . . 8 |
10 | 9 | anbi2i 452 | . . . . . . 7 |
11 | 6, 7, 10 | 3bitr4i 211 | . . . . . 6 |
12 | 2 | brres 4795 | . . . . . 6 |
13 | 11, 12 | bitr4i 186 | . . . . 5 |
14 | 13 | exbii 1569 | . . . 4 |
15 | 4, 5, 14 | 3bitri 205 | . . 3 |
16 | 2 | elrn 4752 | . . 3 |
17 | 2 | elrn 4752 | . . 3 |
18 | 15, 16, 17 | 3bitr4i 211 | . 2 |
19 | 18 | eqriv 2114 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1316 wex 1453 wcel 1465 class class class wbr 3899 crn 4510 cres 4511 ccom 4513 |
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-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 |
This theorem is referenced by: rnco2 5016 cofunexg 5977 1stcof 6029 2ndcof 6030 djudom 6946 |
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