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Mirrors > Home > ILE Home > Th. List > ordin | Unicode version |
Description: The intersection of two ordinal classes is ordinal. Proposition 7.9 of [TakeutiZaring] p. 37. (Contributed by NM, 9-May-1994.) |
Ref | Expression |
---|---|
ordin |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordtr 4396 |
. . 3
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2 | ordtr 4396 |
. . 3
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3 | trin 4126 |
. . 3
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4 | 1, 2, 3 | syl2an 289 |
. 2
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5 | inss2 3371 |
. . 3
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6 | trssord 4398 |
. . 3
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7 | 5, 6 | mp3an2 1336 |
. 2
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8 | 4, 7 | sylancom 420 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-v 2754 df-in 3150 df-ss 3157 df-uni 3825 df-tr 4117 df-iord 4384 |
This theorem is referenced by: onin 4404 smores 6317 smores2 6319 |
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