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Mirrors > Home > ILE Home > Th. List > unrab | Unicode version |
Description: Union of two restricted class abstractions. (Contributed by NM, 25-Mar-2004.) |
Ref | Expression |
---|---|
unrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2402 | . . 3 | |
2 | df-rab 2402 | . . 3 | |
3 | 1, 2 | uneq12i 3198 | . 2 |
4 | df-rab 2402 | . . 3 | |
5 | unab 3313 | . . . 4 | |
6 | andi 792 | . . . . 5 | |
7 | 6 | abbii 2233 | . . . 4 |
8 | 5, 7 | eqtr4i 2141 | . . 3 |
9 | 4, 8 | eqtr4i 2141 | . 2 |
10 | 3, 9 | eqtr4i 2141 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 682 wceq 1316 wcel 1465 cab 2103 crab 2397 cun 3039 |
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-rab 2402 df-v 2662 df-un 3045 |
This theorem is referenced by: rabxmdc 3364 phiprmpw 11825 unennn 11837 znnen 11838 |
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