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Mirrors > Home > ILE Home > Th. List > uniqs | Unicode version |
Description: The union of a quotient set. (Contributed by NM, 9-Dec-2008.) |
Ref | Expression |
---|---|
uniqs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecexg 6401 | . . . . 5 | |
2 | 1 | ralrimivw 2483 | . . . 4 |
3 | dfiun2g 3815 | . . . 4 | |
4 | 2, 3 | syl 14 | . . 3 |
5 | 4 | eqcomd 2123 | . 2 |
6 | df-qs 6403 | . . 3 | |
7 | 6 | unieqi 3716 | . 2 |
8 | df-ec 6399 | . . . . 5 | |
9 | 8 | a1i 9 | . . . 4 |
10 | 9 | iuneq2i 3801 | . . 3 |
11 | imaiun 5629 | . . 3 | |
12 | iunid 3838 | . . . 4 | |
13 | 12 | imaeq2i 4849 | . . 3 |
14 | 10, 11, 13 | 3eqtr2ri 2145 | . 2 |
15 | 5, 7, 14 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 cab 2103 wral 2393 wrex 2394 cvv 2660 csn 3497 cuni 3706 ciun 3783 cima 4512 cec 6395 cqs 6396 |
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-13 1476 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 ax-un 4325 |
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-uni 3707 df-iun 3785 df-br 3900 df-opab 3960 df-xp 4515 df-cnv 4517 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-ec 6399 df-qs 6403 |
This theorem is referenced by: uniqs2 6457 ecqs 6459 |
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