Theorem 2ssom 6787

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 6784	. 2 ⊢ 2o ∈ ω
2		elomssom 4747	. 2 ⊢ (2o ∈ ω → 2o ⊆ ω)
3	1, 2	ax-mp 5	1 ⊢ 2o ⊆ ω

Syntax hints:   ∈ wcel 2209   ⊆ wss 3220  ωcom 4732  2_oc2o 6671

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 623  ax-in2 624  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-14 2212  ax-ext 2220  ax-sep 4244  ax-nul 4254  ax-pow 4306  ax-pr 4341  ax-un 4573  ax-iinf 4730

This theorem depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-ral 2533  df-rex 2534  df-v 2823  df-dif 3222  df-un 3224  df-in 3226  df-ss 3233  df-nul 3521  df-pw 3687  df-sn 3711  df-pr 3712  df-uni 3931  df-int 3966  df-suc 4511  df-iom 4733  df-1o 6677  df-2o 6678

This theorem is referenced by:  2omap  7308  nninfwlporlemd  7502  nninfwlporlem  7503  nninfwlpoimlemg  7505  nninfwlpoimlemginf  7506  nninfctlemfo  12795  bj-charfunbi  16751