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Theorem 2ssom 13448
Description: The ordinal 2 is included in the set of natural number ordinals. (Contributed by BJ, 5-Aug-2024.)
Assertion
Ref Expression
2ssom 2o ⊆ ω

Proof of Theorem 2ssom
StepHypRef Expression
1 2onn 6470 . 2 2o ∈ ω
2 elomssom 4566 . 2 (2o ∈ ω → 2o ⊆ ω)
31, 2ax-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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