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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unab 3404 |
. . 3
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2 | brun 4056 |
. . . . . 6
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3 | 2 | exbii 1605 |
. . . . 5
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4 | 19.43 1628 |
. . . . 5
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5 | 3, 4 | bitr2i 185 |
. . . 4
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6 | 5 | abbii 2293 |
. . 3
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7 | 1, 6 | eqtri 2198 |
. 2
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8 | df-dm 4638 |
. . 3
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9 | df-dm 4638 |
. . 3
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10 | 8, 9 | uneq12i 3289 |
. 2
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11 | df-dm 4638 |
. 2
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12 | 7, 10, 11 | 3eqtr4ri 2209 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2741 df-un 3135 df-br 4006 df-dm 4638 |
This theorem is referenced by: rnun 5039 dmpropg 5103 dmtpop 5106 fntpg 5274 fnun 5324 sbthlemi5 6962 casedm 7087 djudm 7106 exmidfodomrlemim 7202 ennnfonelemhdmp1 12412 ennnfonelemkh 12415 strleund 12564 strleun 12565 |
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