Theorem 2onOLD 8495

Description: Obsolete version of 2on 8494 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 8481	. 2 ⊢ 2o = suc 1o
2		1on 8492	. . 3 ⊢ 1o ∈ On
3	2	onsuci 7833	. 2 ⊢ suc 1o ∈ On
4	1, 3	eqeltri 2830	1 ⊢ 2o ∈ On

Syntax hints:   ∈ wcel 2108  Oncon0 6352  suc csuc 6354  1_oc1o 8473  2_oc2o 8474

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707  ax-sep 5266  ax-nul 5276  ax-pr 5402  ax-un 7729

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-ne 2933  df-ral 3052  df-rex 3061  df-rab 3416  df-v 3461  df-dif 3929  df-un 3931  df-in 3933  df-ss 3943  df-pss 3946  df-nul 4309  df-if 4501  df-pw 4577  df-sn 4602  df-pr 4604  df-op 4608  df-uni 4884  df-br 5120  df-opab 5182  df-tr 5230  df-eprel 5553  df-po 5561  df-so 5562  df-fr 5606  df-we 5608  df-ord 6355  df-on 6356  df-suc 6358  df-1o 8480  df-2o 8481

This theorem is referenced by: (None)