Theorem 1onOLD 8518

Description: Obsolete version of 1on 8517 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 8505	. 2 ⊢ 1o = suc ∅
2		0elon 6440	. . 3 ⊢ ∅ ∈ On
3	2	onsuci 7859	. 2 ⊢ suc ∅ ∈ On
4	1, 3	eqeltri 2835	1 ⊢ 1o ∈ On

Syntax hints:   ∈ wcel 2106  ∅c0 4339  Oncon0 6386  suc csuc 6388  1_oc1o 8498

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438  ax-un 7754

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-pss 3983  df-nul 4340  df-if 4532  df-pw 4607  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-tr 5266  df-eprel 5589  df-po 5597  df-so 5598  df-fr 5641  df-we 5643  df-ord 6389  df-on 6390  df-suc 6392  df-1o 8505

This theorem is referenced by: (None)