Theorem 2ssom 6668

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

Step	Hyp	Ref	Expression
1		2onn 6665	. 2 ⊢ 2o ∈ ω
2		elomssom 4696	. 2 ⊢ (2o ∈ ω → 2o ⊆ ω)
3	1, 2	ax-mp 5	1 ⊢ 2o ⊆ ω

Syntax hints:   ∈ wcel 2200   ⊆ wss 3197  ωcom 4681  2_oc2o 6554

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 617  ax-in2 618  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-13 2202  ax-14 2203  ax-ext 2211  ax-sep 4201  ax-nul 4209  ax-pow 4257  ax-pr 4292  ax-un 4523  ax-iinf 4679

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-rex 2514  df-v 2801  df-dif 3199  df-un 3201  df-in 3203  df-ss 3210  df-nul 3492  df-pw 3651  df-sn 3672  df-pr 3673  df-uni 3888  df-int 3923  df-suc 4461  df-iom 4682  df-1o 6560  df-2o 6561

This theorem is referenced by:  nninfwlporlemd  7335  nninfwlporlem  7336  nninfwlpoimlemg  7338  nninfwlpoimlemginf  7339  nninfctlemfo  12556  bj-charfunbi  16132  2omap  16318