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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 3394 | . . 3 | |
2 | brun 4040 | . . . . . 6 | |
3 | 2 | exbii 1598 | . . . . 5 |
4 | 19.43 1621 | . . . . 5 | |
5 | 3, 4 | bitr2i 184 | . . . 4 |
6 | 5 | abbii 2286 | . . 3 |
7 | 1, 6 | eqtri 2191 | . 2 |
8 | df-dm 4621 | . . 3 | |
9 | df-dm 4621 | . . 3 | |
10 | 8, 9 | uneq12i 3279 | . 2 |
11 | df-dm 4621 | . 2 | |
12 | 7, 10, 11 | 3eqtr4ri 2202 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 703 wceq 1348 wex 1485 cab 2156 cun 3119 class class class wbr 3989 cdm 4611 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-br 3990 df-dm 4621 |
This theorem is referenced by: rnun 5019 dmpropg 5083 dmtpop 5086 fntpg 5254 fnun 5304 sbthlemi5 6938 casedm 7063 djudm 7082 exmidfodomrlemim 7178 ennnfonelemhdmp1 12364 ennnfonelemkh 12367 strleund 12506 strleun 12507 |
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