Theorem 2onOLD 8489

Description: Obsolete version of 2on 8488 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 8475	. 2 ⊢ 2o = suc 1o
2		1on 8486	. . 3 ⊢ 1o ∈ On
3	2	onsuci 7827	. 2 ⊢ suc 1o ∈ On
4	1, 3	eqeltri 2829	1 ⊢ 2o ∈ On

Syntax hints:   ∈ wcel 2107  Oncon0 6349  suc csuc 6351  1_oc1o 8467  2_oc2o 8468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706  ax-sep 5263  ax-nul 5273  ax-pr 5399  ax-un 7723

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-ne 2932  df-ral 3051  df-rex 3060  df-rab 3414  df-v 3459  df-dif 3927  df-un 3929  df-in 3931  df-ss 3941  df-pss 3944  df-nul 4307  df-if 4499  df-pw 4575  df-sn 4600  df-pr 4602  df-op 4606  df-uni 4881  df-br 5117  df-opab 5179  df-tr 5227  df-eprel 5550  df-po 5558  df-so 5559  df-fr 5603  df-we 5605  df-ord 6352  df-on 6353  df-suc 6355  df-1o 8474  df-2o 8475

This theorem is referenced by: (None)