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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 2444 | . 2 | |
2 | df-rab 2444 | . . . 4 | |
3 | df-rab 2444 | . . . 4 | |
4 | 2, 3 | uneq12i 3259 | . . 3 |
5 | elun 3248 | . . . . . . 7 | |
6 | 5 | anbi1i 454 | . . . . . 6 |
7 | andir 809 | . . . . . 6 | |
8 | 6, 7 | bitri 183 | . . . . 5 |
9 | 8 | abbii 2273 | . . . 4 |
10 | unab 3374 | . . . 4 | |
11 | 9, 10 | eqtr4i 2181 | . . 3 |
12 | 4, 11 | eqtr4i 2181 | . 2 |
13 | 1, 12 | eqtr4i 2181 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 698 wceq 1335 wcel 2128 cab 2143 crab 2439 cun 3100 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rab 2444 df-v 2714 df-un 3106 |
This theorem is referenced by: ssfirab 6878 |
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