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Mirrors > Home > ILE Home > Th. List > ordelord | Unicode version |
Description: An element of an ordinal class is ordinal. Proposition 7.6 of [TakeutiZaring] p. 36. (Contributed by NM, 23-Apr-1994.) |
Ref | Expression |
---|---|
ordelord |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2150 |
. . . . 5
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2 | 1 | anbi2d 452 |
. . . 4
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3 | ordeq 4199 |
. . . 4
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4 | 2, 3 | imbi12d 232 |
. . 3
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5 | dford3 4194 |
. . . . . 6
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6 | 5 | simprbi 269 |
. . . . 5
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7 | 6 | r19.21bi 2461 |
. . . 4
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8 | ordelss 4206 |
. . . 4
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9 | simpl 107 |
. . . 4
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10 | trssord 4207 |
. . . 4
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11 | 7, 8, 9, 10 | syl3anc 1174 |
. . 3
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12 | 4, 11 | vtoclg 2679 |
. 2
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13 | 12 | anabsi7 548 |
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-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
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-in 3005 df-ss 3012 df-uni 3654 df-tr 3937 df-iord 4193 |
This theorem is referenced by: tron 4209 ordelon 4210 ordsucg 4319 ordwe 4391 smores 6057 |
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