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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 3348 | . . 3 | |
2 | brun 3987 | . . . . . 6 | |
3 | 2 | exbii 1585 | . . . . 5 |
4 | 19.43 1608 | . . . . 5 | |
5 | 3, 4 | bitr2i 184 | . . . 4 |
6 | 5 | abbii 2256 | . . 3 |
7 | 1, 6 | eqtri 2161 | . 2 |
8 | df-dm 4557 | . . 3 | |
9 | df-dm 4557 | . . 3 | |
10 | 8, 9 | uneq12i 3233 | . 2 |
11 | df-dm 4557 | . 2 | |
12 | 7, 10, 11 | 3eqtr4ri 2172 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 698 wceq 1332 wex 1469 cab 2126 cun 3074 class class class wbr 3937 cdm 4547 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-br 3938 df-dm 4557 |
This theorem is referenced by: rnun 4955 dmpropg 5019 dmtpop 5022 fntpg 5187 fnun 5237 sbthlemi5 6857 casedm 6979 djudm 6998 exmidfodomrlemim 7074 ennnfonelemhdmp1 11958 ennnfonelemkh 11961 strleund 12086 strleun 12087 |
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