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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordtr 4270 | . 2 | |
2 | trss 4005 | . . 3 | |
3 | 2 | imp 123 | . 2 |
4 | 1, 3 | sylan 281 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1465 wss 3041 wtr 3996 word 4254 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-in 3047 df-ss 3054 df-uni 3707 df-tr 3997 df-iord 4258 |
This theorem is referenced by: ordelord 4273 onelss 4279 ordsuc 4448 smores3 6158 tfrlem1 6173 tfrlemisucaccv 6190 tfrlemiubacc 6195 tfr1onlemsucaccv 6206 tfr1onlemubacc 6211 tfrcllemsucaccv 6219 tfrcllemubacc 6224 nntri1 6360 nnsseleq 6365 fict 6730 infnfi 6757 isinfinf 6759 ordiso2 6888 hashinfuni 10491 |
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