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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 3343 | . . 3 | |
2 | brun 3979 | . . . . . 6 | |
3 | 2 | exbii 1584 | . . . . 5 |
4 | 19.43 1607 | . . . . 5 | |
5 | 3, 4 | bitr2i 184 | . . . 4 |
6 | 5 | abbii 2255 | . . 3 |
7 | 1, 6 | eqtri 2160 | . 2 |
8 | df-dm 4549 | . . 3 | |
9 | df-dm 4549 | . . 3 | |
10 | 8, 9 | uneq12i 3228 | . 2 |
11 | df-dm 4549 | . 2 | |
12 | 7, 10, 11 | 3eqtr4ri 2171 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 697 wceq 1331 wex 1468 cab 2125 cun 3069 class class class wbr 3929 cdm 4539 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-br 3930 df-dm 4549 |
This theorem is referenced by: rnun 4947 dmpropg 5011 dmtpop 5014 fntpg 5179 fnun 5229 sbthlemi5 6849 casedm 6971 djudm 6990 exmidfodomrlemim 7057 ennnfonelemhdmp1 11922 ennnfonelemkh 11925 strleund 12047 strleun 12048 |
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