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Mirrors > Home > ILE Home > Th. List > reliun | Unicode version |
Description: An indexed union is a relation iff each member of its indexed family is a relation. (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
reliun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iun 3659 | . . 3 | |
2 | 1 | releqi 4423 | . 2 |
3 | df-rel 4352 | . 2 | |
4 | abss 3009 | . . 3 | |
5 | df-rel 4352 | . . . . . 6 | |
6 | dfss2 2934 | . . . . . 6 | |
7 | 5, 6 | bitri 173 | . . . . 5 |
8 | 7 | ralbii 2330 | . . . 4 |
9 | ralcom4 2576 | . . . 4 | |
10 | r19.23v 2425 | . . . . 5 | |
11 | 10 | albii 1359 | . . . 4 |
12 | 8, 9, 11 | 3bitri 195 | . . 3 |
13 | 4, 12 | bitr4i 176 | . 2 |
14 | 2, 3, 13 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wcel 1393 cab 2026 wral 2306 wrex 2307 cvv 2557 wss 2917 ciun 3657 cxp 4343 wrel 4350 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-in 2924 df-ss 2931 df-iun 3659 df-rel 4352 |
This theorem is referenced by: reluni 4460 eliunxp 4475 opeliunxp2 4476 dfco2 4820 coiun 4830 |
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