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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 2203 |
. . . . 5
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2 | 1 | anbi2d 460 |
. . . 4
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3 | ordeq 4302 |
. . . 4
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4 | 2, 3 | imbi12d 233 |
. . 3
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5 | dford3 4297 |
. . . . . 6
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6 | 5 | simprbi 273 |
. . . . 5
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7 | 6 | r19.21bi 2523 |
. . . 4
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8 | ordelss 4309 |
. . . 4
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9 | simpl 108 |
. . . 4
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10 | trssord 4310 |
. . . 4
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11 | 7, 8, 9, 10 | syl3anc 1217 |
. . 3
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12 | 4, 11 | vtoclg 2749 |
. 2
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13 | 12 | anabsi7 571 |
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-3an 965 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-uni 3745 df-tr 4035 df-iord 4296 |
This theorem is referenced by: tron 4312 ordelon 4313 ordsucg 4426 ordwe 4498 smores 6197 |
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