Theorem 1onOLD 8310

Description: Obsolete version of 1on 8309 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 8297	. 2 ⊢ 1o = suc ∅
2		0elon 6319	. . 3 ⊢ ∅ ∈ On
3	2	onsuci 7685	. 2 ⊢ suc ∅ ∈ On
4	1, 3	eqeltri 2835	1 ⊢ 1o ∈ On

Syntax hints:   ∈ wcel 2106  ∅c0 4256  Oncon0 6266  suc csuc 6268  1_oc1o 8290

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-11 2154  ax-ext 2709  ax-sep 5223  ax-nul 5230  ax-pr 5352  ax-un 7588

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3or 1087  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-ne 2944  df-ral 3069  df-rex 3070  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-pss 3906  df-nul 4257  df-if 4460  df-pw 4535  df-sn 4562  df-pr 4564  df-op 4568  df-uni 4840  df-br 5075  df-opab 5137  df-tr 5192  df-eprel 5495  df-po 5503  df-so 5504  df-fr 5544  df-we 5546  df-ord 6269  df-on 6270  df-suc 6272  df-1o 8297

This theorem is referenced by: (None)