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Mirrors > Home > ILE Home > Th. List > dfiun2g | Unicode version |
Description: Alternate definition of
indexed union when ![]() |
Ref | Expression |
---|---|
dfiun2g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2469 |
. . . . . 6
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2 | rsp 2483 |
. . . . . . . 8
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3 | clel3g 2823 |
. . . . . . . 8
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4 | 2, 3 | syl6 33 |
. . . . . . 7
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5 | 4 | imp 123 |
. . . . . 6
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6 | 1, 5 | rexbida 2433 |
. . . . 5
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7 | rexcom4 2712 |
. . . . 5
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8 | 6, 7 | syl6bb 195 |
. . . 4
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9 | r19.41v 2590 |
. . . . . 6
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10 | 9 | exbii 1585 |
. . . . 5
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11 | exancom 1588 |
. . . . 5
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12 | 10, 11 | bitri 183 |
. . . 4
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13 | 8, 12 | syl6bb 195 |
. . 3
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14 | eliun 3825 |
. . 3
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15 | eluniab 3756 |
. . 3
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16 | 13, 14, 15 | 3bitr4g 222 |
. 2
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17 | 16 | eqrdv 2138 |
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 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-ral 2422 df-rex 2423 df-v 2691 df-uni 3745 df-iun 3823 |
This theorem is referenced by: dfiun2 3855 abnexg 4375 dfiun3g 4804 fniunfv 5671 iunexg 6025 uniqs 6495 iunopn 12208 |
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