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Mirrors > Home > ILE Home > Th. List > dfiun2g | Unicode version |
Description: Alternate definition of indexed union when is a set. Definition 15(a) of [Suppes] p. 44. (Contributed by NM, 23-Mar-2006.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
dfiun2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2355 | . . . . . 6 | |
2 | rsp 2369 | . . . . . . . 8 | |
3 | clel3g 2678 | . . . . . . . 8 | |
4 | 2, 3 | syl6 29 | . . . . . . 7 |
5 | 4 | imp 115 | . . . . . 6 |
6 | 1, 5 | rexbida 2321 | . . . . 5 |
7 | rexcom4 2577 | . . . . 5 | |
8 | 6, 7 | syl6bb 185 | . . . 4 |
9 | r19.41v 2466 | . . . . . 6 | |
10 | 9 | exbii 1496 | . . . . 5 |
11 | exancom 1499 | . . . . 5 | |
12 | 10, 11 | bitri 173 | . . . 4 |
13 | 8, 12 | syl6bb 185 | . . 3 |
14 | eliun 3661 | . . 3 | |
15 | eluniab 3592 | . . 3 | |
16 | 13, 14, 15 | 3bitr4g 212 | . 2 |
17 | 16 | eqrdv 2038 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 cab 2026 wral 2306 wrex 2307 cuni 3580 ciun 3657 |
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-uni 3581 df-iun 3659 |
This theorem is referenced by: dfiun2 3691 dfiun3g 4589 fniunfv 5401 iunexg 5746 uniqs 6164 |
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