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Mirrors > Home > ILE Home > Th. List > dmun | Unicode version |
Description: The domain of a union is the union of domains. Exercise 56(a) of [Enderton] p. 65. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
dmun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unab 3374 | . . 3 | |
2 | brun 4016 | . . . . . 6 | |
3 | 2 | exbii 1585 | . . . . 5 |
4 | 19.43 1608 | . . . . 5 | |
5 | 3, 4 | bitr2i 184 | . . . 4 |
6 | 5 | abbii 2273 | . . 3 |
7 | 1, 6 | eqtri 2178 | . 2 |
8 | df-dm 4597 | . . 3 | |
9 | df-dm 4597 | . . 3 | |
10 | 8, 9 | uneq12i 3259 | . 2 |
11 | df-dm 4597 | . 2 | |
12 | 7, 10, 11 | 3eqtr4ri 2189 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 698 wceq 1335 wex 1472 cab 2143 cun 3100 class class class wbr 3966 cdm 4587 |
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-v 2714 df-un 3106 df-br 3967 df-dm 4597 |
This theorem is referenced by: rnun 4995 dmpropg 5059 dmtpop 5062 fntpg 5227 fnun 5277 sbthlemi5 6906 casedm 7031 djudm 7050 exmidfodomrlemim 7137 ennnfonelemhdmp1 12180 ennnfonelemkh 12183 strleund 12320 strleun 12321 |
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