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Mirrors > Home > ILE Home > Th. List > 1oex | GIF version |
Description: Ordinal 1 is a set. (Contributed by BJ, 4-Jul-2022.) |
Ref | Expression |
---|---|
1oex | ⊢ 1o ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1on 6288 | . 2 ⊢ 1o ∈ On | |
2 | 1 | elexi 2672 | 1 ⊢ 1o ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 Vcvv 2660 Oncon0 4255 1oc1o 6274 |
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-sep 4016 ax-nul 4024 ax-pow 4068 ax-pr 4101 ax-un 4325 |
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-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-uni 3707 df-tr 3997 df-iord 4258 df-on 4260 df-suc 4263 df-1o 6281 |
This theorem is referenced by: 1lt2o 6307 map1 6674 1domsn 6681 djuexb 6897 djurclr 6903 djurcl 6905 djurf1or 6910 djurf1o 6912 djuss 6923 infnninf 6990 nnnninf 6991 ismkvnex 6997 dju1p1e2 7021 exmidfodomrlemr 7026 exmidfodomrlemrALT 7027 djucomen 7040 djuassen 7041 indpi 7118 prarloclemlt 7269 fxnn0nninf 10179 inftonninf 10182 enctlem 11872 djurclALT 12936 pwle2 13120 |
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