Theorem 2onOLD 8521

Description: Obsolete version of 2on 8520 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 8507	. 2 ⊢ 2o = suc 1o
2		1on 8518	. . 3 ⊢ 1o ∈ On
3	2	onsuci 7859	. 2 ⊢ suc 1o ∈ On
4	1, 3	eqeltri 2837	1 ⊢ 2o ∈ On

Syntax hints:   ∈ wcel 2108  Oncon0 6384  suc csuc 6386  1_oc1o 8499  2_oc2o 8500

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 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432  ax-un 7755

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3or 1088  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-pss 3971  df-nul 4334  df-if 4526  df-pw 4602  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-tr 5260  df-eprel 5584  df-po 5592  df-so 5593  df-fr 5637  df-we 5639  df-ord 6387  df-on 6388  df-suc 6390  df-1o 8506  df-2o 8507

This theorem is referenced by: (None)