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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nnord | Unicode version |
Description: A natural number is an ordinal. Constructive proof of nnord 4495. Can also be proved from bj-nnelon 13084 if the latter is proved from bj-omssonALT 13088. (Contributed by BJ, 27-Oct-2020.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nnord |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nntrans2 13077 | . 2 | |
2 | bj-omtrans 13081 | . . . . . 6 | |
3 | 2 | sseld 3066 | . . . . 5 |
4 | bj-nntrans2 13077 | . . . . 5 | |
5 | 3, 4 | syl6 33 | . . . 4 |
6 | 5 | alrimiv 1830 | . . 3 |
7 | df-ral 2398 | . . 3 | |
8 | 6, 7 | sylibr 133 | . 2 |
9 | dford3 4259 | . 2 | |
10 | 1, 8, 9 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1314 wcel 1465 wral 2393 wtr 3996 word 4254 com 4474 |
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-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-nul 4024 ax-pr 4101 ax-un 4325 ax-bd0 12938 ax-bdor 12941 ax-bdal 12943 ax-bdex 12944 ax-bdeq 12945 ax-bdel 12946 ax-bdsb 12947 ax-bdsep 13009 ax-infvn 13066 |
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-rab 2402 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-sn 3503 df-pr 3504 df-uni 3707 df-int 3742 df-tr 3997 df-iord 4258 df-suc 4263 df-iom 4475 df-bdc 12966 df-bj-ind 13052 |
This theorem is referenced by: bj-nnelon 13084 |
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