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Mirrors > Home > ILE Home > Th. List > iunxiun | Unicode version |
Description: Separate an indexed union in the index of an indexed union. (Contributed by Mario Carneiro, 5-Dec-2016.) |
Ref | Expression |
---|---|
iunxiun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eliun 3690 |
. . . . . . . 8
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2 | 1 | anbi1i 446 |
. . . . . . 7
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3 | r19.41v 2511 |
. . . . . . 7
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4 | 2, 3 | bitr4i 185 |
. . . . . 6
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5 | 4 | exbii 1537 |
. . . . 5
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6 | rexcom4 2623 |
. . . . 5
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7 | 5, 6 | bitr4i 185 |
. . . 4
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8 | df-rex 2355 |
. . . 4
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9 | eliun 3690 |
. . . . . 6
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10 | df-rex 2355 |
. . . . . 6
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11 | 9, 10 | bitri 182 |
. . . . 5
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12 | 11 | rexbii 2374 |
. . . 4
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13 | 7, 8, 12 | 3bitr4i 210 |
. . 3
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14 | eliun 3690 |
. . 3
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15 | eliun 3690 |
. . 3
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16 | 13, 14, 15 | 3bitr4i 210 |
. 2
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17 | 16 | eqriv 2079 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-ral 2354 df-rex 2355 df-v 2604 df-iun 3688 |
This theorem is referenced by: (None) |
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