Theorem bj-2ex 32939

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 7561	. 2 ⊢ 2𝑜 = suc 1𝑜
2		bj-1ex 32938	. . 3 ⊢ 1𝑜 ∈ V
3	2	sucex 7011	. 2 ⊢ suc 1𝑜 ∈ V
4	1, 3	eqeltri 2697	1 ⊢ 2𝑜 ∈ V

Syntax hints:   ∈ wcel 1990  Vcvv 3200  suc csuc 5725  1_𝑜c1o 7553  2_𝑜c2o 7554

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pr 4906  ax-un 6949

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rex 2918  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-sn 4178  df-pr 4180  df-uni 4437  df-suc 5729  df-1o 7560  df-2o 7561

This theorem is referenced by: (None)