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Mirrors > Home > ILE Home > Th. List > iunid | Unicode version |
Description: An indexed union of singletons recovers the index set. (Contributed by NM, 6-Sep-2005.) |
Ref | Expression |
---|---|
iunid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sn 3587 | . . . . 5 | |
2 | equcom 1699 | . . . . . 6 | |
3 | 2 | abbii 2286 | . . . . 5 |
4 | 1, 3 | eqtri 2191 | . . . 4 |
5 | 4 | a1i 9 | . . 3 |
6 | 5 | iuneq2i 3889 | . 2 |
7 | iunab 3917 | . . 3 | |
8 | risset 2498 | . . . 4 | |
9 | 8 | abbii 2286 | . . 3 |
10 | abid2 2291 | . . 3 | |
11 | 7, 9, 10 | 3eqtr2i 2197 | . 2 |
12 | 6, 11 | eqtri 2191 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 wcel 2141 cab 2156 wrex 2449 csn 3581 ciun 3871 |
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-sn 3587 df-iun 3873 |
This theorem is referenced by: abnexg 4429 iunxpconst 4669 xpexgALT 6109 uniqs 6567 |
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