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Mirrors > Home > ILE Home > Th. List > Mathboxes > 2ssom | GIF version |
Description: The ordinal 2 is included in the set of natural number ordinals. (Contributed by BJ, 5-Aug-2024.) |
Ref | Expression |
---|---|
2ssom | ⊢ 2o ⊆ ω |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2onn 6470 | . 2 ⊢ 2o ∈ ω | |
2 | elomssom 4566 | . 2 ⊢ (2o ∈ ω → 2o ⊆ ω) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 2o ⊆ ω |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 ⊆ wss 3102 ωcom 4551 2oc2o 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 ax-iinf 4549 |
This theorem depends on definitions: df-bi 116 df-3an 965 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-int 3810 df-suc 4333 df-iom 4552 df-1o 6365 df-2o 6366 |
This theorem is referenced by: bj-charfunbi 13457 |
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