Theorem 2onOLD 8477

Description: Obsolete version of 2on 8476 as of 30-Nov-2024. (Contributed by NM, 18-Feb-2004.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
2onOLD	⊢ 2o ∈ On

Proof of Theorem 2onOLD

Step	Hyp	Ref	Expression
1		df-2o 8463	. 2 ⊢ 2o = suc 1o
2		1on 8474	. . 3 ⊢ 1o ∈ On
3	2	onsuci 7821	. 2 ⊢ suc 1o ∈ On
4	1, 3	eqeltri 2821	1 ⊢ 2o ∈ On

Syntax hints:   ∈ wcel 2098  Oncon0 6355  suc csuc 6357  1_oc1o 8455  2_oc2o 8456

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418  ax-un 7719

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3or 1085  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-pss 3960  df-nul 4316  df-if 4522  df-pw 4597  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-opab 5202  df-tr 5257  df-eprel 5571  df-po 5579  df-so 5580  df-fr 5622  df-we 5624  df-ord 6358  df-on 6359  df-suc 6361  df-1o 8462  df-2o 8463

This theorem is referenced by: (None)