Theorem 1onOLD 8508

Description: Obsolete version of 1on 8507 as of 30-Nov-2024. (Contributed by NM, 29-Oct-1995.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
1onOLD	⊢ 1o ∈ On

Proof of Theorem 1onOLD

Step	Hyp	Ref	Expression
1		df-1o 8495	. 2 ⊢ 1o = suc ∅
2		0elon 6429	. . 3 ⊢ ∅ ∈ On
3	2	onsuci 7847	. 2 ⊢ suc ∅ ∈ On
4	1, 3	eqeltri 2821	1 ⊢ 1o ∈ On

Syntax hints:   ∈ wcel 2098  ∅c0 4324  Oncon0 6375  suc csuc 6377  1_oc1o 8488

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 2696  ax-sep 5303  ax-nul 5310  ax-pr 5432  ax-un 7745

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3or 1085  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ne 2930  df-ral 3051  df-rex 3060  df-rab 3419  df-v 3463  df-dif 3949  df-un 3951  df-in 3953  df-ss 3963  df-pss 3966  df-nul 4325  df-if 4533  df-pw 4608  df-sn 4633  df-pr 4635  df-op 4639  df-uni 4913  df-br 5153  df-opab 5215  df-tr 5270  df-eprel 5585  df-po 5593  df-so 5594  df-fr 5636  df-we 5638  df-ord 6378  df-on 6379  df-suc 6381  df-1o 8495

This theorem is referenced by: (None)