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Mirrors > Home > MPE Home > Th. List > reliun | Structured version Visualization version 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 4280 |
. . 3
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2 | 1 | releqi 4918 |
. 2
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3 | df-rel 4841 |
. 2
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4 | abss 3498 |
. . 3
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5 | df-rel 4841 |
. . . . . 6
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6 | dfss2 3421 |
. . . . . 6
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7 | 5, 6 | bitri 253 |
. . . . 5
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8 | 7 | ralbii 2819 |
. . . 4
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9 | ralcom4 3066 |
. . . 4
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10 | r19.23v 2867 |
. . . . 5
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11 | 10 | albii 1691 |
. . . 4
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12 | 8, 9, 11 | 3bitri 275 |
. . 3
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13 | 4, 12 | bitr4i 256 |
. 2
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14 | 2, 3, 13 | 3bitri 275 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ral 2742 df-rex 2743 df-v 3047 df-in 3411 df-ss 3418 df-iun 4280 df-rel 4841 |
This theorem is referenced by: reluni 4956 eliunxp 4972 opeliunxp2 4973 dfco2 5334 coiun 5345 fvn0ssdmfun 6013 opeliunxp2f 6956 fsumcom2 13835 fprodcom2 14038 imasaddfnlem 15434 imasvscafn 15443 gsum2d2lem 17605 gsum2d2 17606 gsumcom2 17607 dprd2d2 17677 cnextrel 21078 reldv 22825 dfcnv2 28279 cvmliftlem1 30008 cnviun 36242 coiun1 36244 eliunxp2 40168 |
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