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Mirrors > Home > ILE Home > Th. List > rniun | Unicode version |
Description: The range of an indexed union. (Contributed by Mario Carneiro, 29-May-2015.) |
Ref | Expression |
---|---|
rniun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexcom4 2772 |
. . . 4
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2 | vex 2752 |
. . . . . 6
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3 | 2 | elrn2 4881 |
. . . . 5
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4 | 3 | rexbii 2494 |
. . . 4
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5 | eliun 3902 |
. . . . 5
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6 | 5 | exbii 1615 |
. . . 4
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7 | 1, 4, 6 | 3bitr4ri 213 |
. . 3
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8 | 2 | elrn2 4881 |
. . 3
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9 | eliun 3902 |
. . 3
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10 | 7, 8, 9 | 3bitr4i 212 |
. 2
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11 | 10 | 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-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-iun 3900 df-br 4016 df-opab 4077 df-cnv 4646 df-dm 4648 df-rn 4649 |
This theorem is referenced by: rnuni 5052 fun11iun 5494 ennnfonelemrn 12434 |
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