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Mirrors > Home > ILE Home > Th. List > unon | Unicode version |
Description: The class of all ordinal numbers is its own union. Exercise 11 of [TakeutiZaring] p. 40. (Contributed by NM, 12-Nov-2003.) |
Ref | Expression |
---|---|
unon |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluni2 3655 |
. . . 4
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2 | onelon 4209 |
. . . . 5
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3 | 2 | rexlimiva 2484 |
. . . 4
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4 | 1, 3 | sylbi 119 |
. . 3
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5 | vex 2622 |
. . . . 5
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6 | 5 | sucid 4242 |
. . . 4
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7 | suceloni 4316 |
. . . 4
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8 | elunii 3656 |
. . . 4
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9 | 6, 7, 8 | sylancr 405 |
. . 3
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10 | 4, 9 | impbii 124 |
. 2
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11 | 10 | eqriv 2085 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3955 ax-pow 4007 ax-pr 4034 ax-un 4258 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-pw 3429 df-sn 3450 df-pr 3451 df-uni 3652 df-tr 3935 df-iord 4191 df-on 4193 df-suc 4196 |
This theorem is referenced by: limon 4328 onintonm 4332 tfri1dALT 6108 rdgon 6143 |
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