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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 3873 | . . 3 | |
2 | 1 | releqi 4692 | . 2 |
3 | df-rel 4616 | . 2 | |
4 | abss 3216 | . . 3 | |
5 | df-rel 4616 | . . . . . 6 | |
6 | dfss2 3136 | . . . . . 6 | |
7 | 5, 6 | bitri 183 | . . . . 5 |
8 | 7 | ralbii 2476 | . . . 4 |
9 | ralcom4 2752 | . . . 4 | |
10 | r19.23v 2579 | . . . . 5 | |
11 | 10 | albii 1463 | . . . 4 |
12 | 8, 9, 11 | 3bitri 205 | . . 3 |
13 | 4, 12 | bitr4i 186 | . 2 |
14 | 2, 3, 13 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1346 wcel 2141 cab 2156 wral 2448 wrex 2449 cvv 2730 wss 3121 ciun 3871 cxp 4607 wrel 4614 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-in 3127 df-ss 3134 df-iun 3873 df-rel 4616 |
This theorem is referenced by: reluni 4732 eliunxp 4748 opeliunxp2 4749 dfco2 5108 coiun 5118 opeliunxp2f 6214 fisumcom2 11388 fprodcom2fi 11576 reldvg 13401 |
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