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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 3663 |
. . . 4
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2 | onelon 4220 |
. . . . 5
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3 | 2 | rexlimiva 2485 |
. . . 4
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4 | 1, 3 | sylbi 120 |
. . 3
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5 | vex 2623 |
. . . . 5
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6 | 5 | sucid 4253 |
. . . 4
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7 | suceloni 4331 |
. . . 4
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8 | elunii 3664 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 6, 7, 8 | sylancr 406 |
. . 3
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10 | 4, 9 | impbii 125 |
. 2
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11 | 10 | eqriv 2086 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-13 1450 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 ax-un 4269 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-uni 3660 df-tr 3943 df-iord 4202 df-on 4204 df-suc 4207 |
This theorem is referenced by: limon 4343 onintonm 4347 tfri1dALT 6130 rdgon 6165 |
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