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Mirrors > Home > ILE Home > Th. List > rabun2 | Unicode version |
Description: Abstraction restricted to a union. (Contributed by Stefan O'Rear, 5-Feb-2015.) |
Ref | Expression |
---|---|
rabun2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2315 | . 2 | |
2 | df-rab 2315 | . . . 4 | |
3 | df-rab 2315 | . . . 4 | |
4 | 2, 3 | uneq12i 3095 | . . 3 |
5 | elun 3084 | . . . . . . 7 | |
6 | 5 | anbi1i 431 | . . . . . 6 |
7 | andir 732 | . . . . . 6 | |
8 | 6, 7 | bitri 173 | . . . . 5 |
9 | 8 | abbii 2153 | . . . 4 |
10 | unab 3204 | . . . 4 | |
11 | 9, 10 | eqtr4i 2063 | . . 3 |
12 | 4, 11 | eqtr4i 2063 | . 2 |
13 | 1, 12 | eqtr4i 2063 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wo 629 wceq 1243 wcel 1393 cab 2026 crab 2310 cun 2915 |
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-rab 2315 df-v 2559 df-un 2922 |
This theorem is referenced by: (None) |
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