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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 2443 | . . . . . 6 | |
2 | rsp 2457 | . . . . . . . 8 | |
3 | clel3g 2793 | . . . . . . . 8 | |
4 | 2, 3 | syl6 33 | . . . . . . 7 |
5 | 4 | imp 123 | . . . . . 6 |
6 | 1, 5 | rexbida 2409 | . . . . 5 |
7 | rexcom4 2683 | . . . . 5 | |
8 | 6, 7 | syl6bb 195 | . . . 4 |
9 | r19.41v 2564 | . . . . . 6 | |
10 | 9 | exbii 1569 | . . . . 5 |
11 | exancom 1572 | . . . . 5 | |
12 | 10, 11 | bitri 183 | . . . 4 |
13 | 8, 12 | syl6bb 195 | . . 3 |
14 | eliun 3787 | . . 3 | |
15 | eluniab 3718 | . . 3 | |
16 | 13, 14, 15 | 3bitr4g 222 | . 2 |
17 | 16 | eqrdv 2115 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wex 1453 wcel 1465 cab 2103 wral 2393 wrex 2394 cuni 3706 ciun 3783 |
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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-uni 3707 df-iun 3785 |
This theorem is referenced by: dfiun2 3817 abnexg 4337 dfiun3g 4766 fniunfv 5631 iunexg 5985 uniqs 6455 iunopn 12096 |
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