Theorem 1onOLD 8381

Description: Obsolete version of 1on 8380 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 8368	. 2 ⊢ 1o = suc ∅
2		0elon 6356	. . 3 ⊢ ∅ ∈ On
3	2	onsuci 7753	. 2 ⊢ suc ∅ ∈ On
4	1, 3	eqeltri 2833	1 ⊢ 1o ∈ On

Syntax hints:   ∈ wcel 2105  ∅c0 4270  Oncon0 6303  suc csuc 6305  1_oc1o 8361

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707  ax-sep 5244  ax-nul 5251  ax-pr 5373  ax-un 7651

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3or 1087  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3404  df-v 3443  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-pss 3917  df-nul 4271  df-if 4475  df-pw 4550  df-sn 4575  df-pr 4577  df-op 4581  df-uni 4854  df-br 5094  df-opab 5156  df-tr 5211  df-eprel 5525  df-po 5533  df-so 5534  df-fr 5576  df-we 5578  df-ord 6306  df-on 6307  df-suc 6309  df-1o 8368

This theorem is referenced by: (None)