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Mirrors > Home > ILE Home > Th. List > ordelss | Unicode version |
Description: An element of an ordinal class is a subset of it. (Contributed by NM, 30-May-1994.) |
Ref | Expression |
---|---|
ordelss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordtr 4308 |
. 2
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2 | trss 4043 |
. . 3
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3 | 2 | imp 123 |
. 2
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4 | 1, 3 | sylan 281 |
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-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-v 2691 df-in 3082 df-ss 3089 df-uni 3745 df-tr 4035 df-iord 4296 |
This theorem is referenced by: ordelord 4311 onelss 4317 ordsuc 4486 smores3 6198 tfrlem1 6213 tfrlemisucaccv 6230 tfrlemiubacc 6235 tfr1onlemsucaccv 6246 tfr1onlemubacc 6251 tfrcllemsucaccv 6259 tfrcllemubacc 6264 nntri1 6400 nnsseleq 6405 fict 6770 infnfi 6797 isinfinf 6799 ordiso2 6928 hashinfuni 10555 |
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