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Mirrors > Home > ILE Home > Th. List > iuncom4 | Unicode version |
Description: Commutation of union with indexed union. (Contributed by Mario Carneiro, 18-Jan-2014.) |
Ref | Expression |
---|---|
iuncom4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2471 |
. . . . . . 7
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2 | 1 | rexbii 2494 |
. . . . . 6
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3 | rexcom4 2772 |
. . . . . 6
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4 | 2, 3 | bitri 184 |
. . . . 5
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5 | r19.41v 2643 |
. . . . . 6
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6 | 5 | exbii 1615 |
. . . . 5
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7 | 4, 6 | bitri 184 |
. . . 4
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8 | eluni2 3825 |
. . . . 5
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9 | 8 | rexbii 2494 |
. . . 4
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10 | df-rex 2471 |
. . . . 5
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11 | eliun 3902 |
. . . . . . 7
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12 | 11 | anbi1i 458 |
. . . . . 6
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13 | 12 | exbii 1615 |
. . . . 5
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14 | 10, 13 | bitri 184 |
. . . 4
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15 | 7, 9, 14 | 3bitr4i 212 |
. . 3
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16 | eliun 3902 |
. . 3
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17 | eluni2 3825 |
. . 3
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18 | 15, 16, 17 | 3bitr4i 212 |
. 2
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19 | 18 | eqriv 2184 |
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 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-uni 3822 df-iun 3900 |
This theorem is referenced by: tgidm 13845 |
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