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Mirrors > Home > ILE Home > Th. List > 2on | Unicode version |
Description: Ordinal 2 is an ordinal number. (Contributed by NM, 18-Feb-2004.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) |
Ref | Expression |
---|---|
2on |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 6366 | . 2 | |
2 | 1on 6372 | . . 3 | |
3 | 2 | onsuci 4477 | . 2 |
4 | 1, 3 | eqeltri 2230 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2128 con0 4325 csuc 4327 c1o 6358 c2o 6359 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-nul 4092 ax-pow 4137 ax-pr 4171 ax-un 4395 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3396 df-pw 3546 df-sn 3567 df-pr 3568 df-uni 3775 df-tr 4065 df-iord 4328 df-on 4330 df-suc 4333 df-1o 6365 df-2o 6366 |
This theorem is referenced by: 3on 6376 infnninf 7069 onntri35 7174 bj-charfunbi 13457 |
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