Theorem bj-2ex 33237

Description: 2_𝑜 is a set. (Contributed by BJ, 6-Apr-2019.)

Assertion

Ref	Expression
bj-2ex	⊢ 2𝑜 ∈ V

Proof of Theorem bj-2ex

Step	Hyp	Ref	Expression
1		df-2o 7722	. 2 ⊢ 2𝑜 = suc 1𝑜
2		bj-1ex 33236	. . 3 ⊢ 1𝑜 ∈ V
3	2	sucex 7168	. 2 ⊢ suc 1𝑜 ∈ V
4	1, 3	eqeltri 2827	1 ⊢ 2𝑜 ∈ V

Syntax hints:   ∈ wcel 2131  Vcvv 3332  suc csuc 5878  1_𝑜c1o 7714  2_𝑜c2o 7715

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878  ax-5 1980  ax-6 2046  ax-7 2082  ax-8 2133  ax-9 2140  ax-10 2160  ax-11 2175  ax-12 2188  ax-13 2383  ax-ext 2732  ax-sep 4925  ax-nul 4933  ax-pr 5047  ax-un 7106

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1627  df-ex 1846  df-nf 1851  df-sb 2039  df-clab 2739  df-cleq 2745  df-clel 2748  df-nfc 2883  df-rex 3048  df-v 3334  df-dif 3710  df-un 3712  df-in 3714  df-ss 3721  df-nul 4051  df-sn 4314  df-pr 4316  df-uni 4581  df-suc 5882  df-1o 7721  df-2o 7722

This theorem is referenced by: (None)