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Mirrors > Home > ILE Home > Th. List > coiun | Unicode version |
Description: Composition with an indexed union. (Contributed by NM, 21-Dec-2008.) |
Ref | Expression |
---|---|
coiun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relco 5007 | . 2 | |
2 | reliun 4630 | . . 3 | |
3 | relco 5007 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | 2, 4 | mprgbir 2467 | . 2 |
6 | eliun 3787 | . . . . . . . 8 | |
7 | df-br 3900 | . . . . . . . 8 | |
8 | df-br 3900 | . . . . . . . . 9 | |
9 | 8 | rexbii 2419 | . . . . . . . 8 |
10 | 6, 7, 9 | 3bitr4i 211 | . . . . . . 7 |
11 | 10 | anbi1i 453 | . . . . . 6 |
12 | r19.41v 2564 | . . . . . 6 | |
13 | 11, 12 | bitr4i 186 | . . . . 5 |
14 | 13 | exbii 1569 | . . . 4 |
15 | rexcom4 2683 | . . . 4 | |
16 | 14, 15 | bitr4i 186 | . . 3 |
17 | vex 2663 | . . . 4 | |
18 | vex 2663 | . . . 4 | |
19 | 17, 18 | opelco 4681 | . . 3 |
20 | eliun 3787 | . . . 4 | |
21 | 17, 18 | opelco 4681 | . . . . 5 |
22 | 21 | rexbii 2419 | . . . 4 |
23 | 20, 22 | bitri 183 | . . 3 |
24 | 16, 19, 23 | 3bitr4i 211 | . 2 |
25 | 1, 5, 24 | eqrelriiv 4603 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1316 wex 1453 wcel 1465 wrex 2394 cop 3500 ciun 3783 class class class wbr 3899 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-iun 3785 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-co 4518 |
This theorem is referenced by: (None) |
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