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Mirrors > Home > ILE Home > Th. List > 0elon | Unicode version |
Description: The empty set is an ordinal number. Corollary 7N(b) of [Enderton] p. 193. (Contributed by NM, 17-Sep-1993.) |
Ref | Expression |
---|---|
0elon |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ord0 4283 | . 2 | |
2 | 0ex 4025 | . . 3 | |
3 | 2 | elon 4266 | . 2 |
4 | 1, 3 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 c0 3333 word 4254 con0 4255 |
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-in1 588 ax-in2 589 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 ax-nul 4024 |
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-rex 2399 df-v 2662 df-dif 3043 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-uni 3707 df-tr 3997 df-iord 4258 df-on 4260 |
This theorem is referenced by: inton 4285 onn0 4292 onm 4293 limon 4399 ordtriexmid 4407 ordtri2orexmid 4408 onsucsssucexmid 4412 onsucelsucexmid 4415 ordsoexmid 4447 ordpwsucexmid 4455 ordtri2or2exmid 4456 tfr0dm 6187 1on 6288 ordgt0ge1 6300 omv 6319 oa0 6321 om0 6322 oei0 6323 omcl 6325 omv2 6329 oaword1 6335 nna0r 6342 nnm0r 6343 card0 7012 |
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