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Mirrors > Home > ILE Home > Th. List > dmuni | Unicode version |
Description: The domain of a union. Part of Exercise 8 of [Enderton] p. 41. (Contributed by NM, 3-Feb-2004.) |
Ref | Expression |
---|---|
dmuni |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1664 |
. . . . 5
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2 | ancom 266 |
. . . . . . 7
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3 | 19.41v 1902 |
. . . . . . 7
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4 | vex 2740 |
. . . . . . . . 9
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5 | 4 | eldm2 4821 |
. . . . . . . 8
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6 | 5 | anbi2i 457 |
. . . . . . 7
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7 | 2, 3, 6 | 3bitr4i 212 |
. . . . . 6
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8 | 7 | exbii 1605 |
. . . . 5
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9 | 1, 8 | bitri 184 |
. . . 4
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10 | eluni 3810 |
. . . . 5
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11 | 10 | exbii 1605 |
. . . 4
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12 | df-rex 2461 |
. . . 4
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13 | 9, 11, 12 | 3bitr4i 212 |
. . 3
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14 | 4 | eldm2 4821 |
. . 3
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15 | eliun 3888 |
. . 3
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16 | 13, 14, 15 | 3bitr4i 212 |
. 2
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17 | 16 | eqriv 2174 |
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-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-iun 3886 df-br 4001 df-dm 4633 |
This theorem is referenced by: tfrlem8 6313 tfrlemi14d 6328 tfr1onlemres 6344 tfrcllemres 6357 |
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