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Mirrors > Home > ILE Home > Th. List > reliun | Unicode version |
Description: An indexed union is a relation iff each member of its indexed family is a relation. (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
reliun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iun 3823 |
. . 3
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2 | 1 | releqi 4630 |
. 2
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3 | df-rel 4554 |
. 2
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4 | abss 3171 |
. . 3
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5 | df-rel 4554 |
. . . . . 6
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6 | dfss2 3091 |
. . . . . 6
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7 | 5, 6 | bitri 183 |
. . . . 5
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8 | 7 | ralbii 2444 |
. . . 4
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9 | ralcom4 2711 |
. . . 4
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10 | r19.23v 2544 |
. . . . 5
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11 | 10 | albii 1447 |
. . . 4
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12 | 8, 9, 11 | 3bitri 205 |
. . 3
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13 | 4, 12 | bitr4i 186 |
. 2
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14 | 2, 3, 13 | 3bitri 205 |
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-in 3082 df-ss 3089 df-iun 3823 df-rel 4554 |
This theorem is referenced by: reluni 4670 eliunxp 4686 opeliunxp2 4687 dfco2 5046 coiun 5056 opeliunxp2f 6143 fisumcom2 11239 reldvg 12856 |
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