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Mirrors > Home > ILE Home > Th. List > 3on | GIF version |
Description: Ordinal 3 is an ordinal number. (Contributed by Mario Carneiro, 5-Jan-2016.) |
Ref | Expression |
---|---|
3on | ⊢ 3o ∈ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3o 6267 | . 2 ⊢ 3o = suc 2o | |
2 | 2on 6274 | . . 3 ⊢ 2o ∈ On | |
3 | 2 | onsuci 4390 | . 2 ⊢ suc 2o ∈ On |
4 | 1, 3 | eqeltri 2185 | 1 ⊢ 3o ∈ On |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1461 Oncon0 4243 suc csuc 4245 2oc2o 6259 3oc3o 6260 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-13 1472 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-nul 4012 ax-pow 4056 ax-pr 4089 ax-un 4313 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-dif 3037 df-un 3039 df-in 3041 df-ss 3048 df-nul 3328 df-pw 3476 df-sn 3497 df-pr 3498 df-uni 3701 df-tr 3985 df-iord 4246 df-on 4248 df-suc 4251 df-1o 6265 df-2o 6266 df-3o 6267 |
This theorem is referenced by: 4on 6277 |
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