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Mirrors > Home > ILE Home > Th. List > iunxun | Unicode version |
Description: Separate a union in the index of an indexed union. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) |
Ref | Expression |
---|---|
iunxun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexun 3327 |
. . . 4
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2 | eliun 3902 |
. . . . 5
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3 | eliun 3902 |
. . . . 5
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4 | 2, 3 | orbi12i 765 |
. . . 4
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5 | 1, 4 | bitr4i 187 |
. . 3
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6 | eliun 3902 |
. . 3
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7 | elun 3288 |
. . 3
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8 | 5, 6, 7 | 3bitr4i 212 |
. 2
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9 | 8 | 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-un 3145 df-iun 3900 |
This theorem is referenced by: iunxprg 3979 iunsuc 4432 rdgisuc1 6399 oasuc 6479 omsuc 6487 iunfidisj 6959 fsum2dlemstep 11456 fsumiun 11499 fprod2dlemstep 11644 iuncld 13911 |
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