Theorem bj-2ex 32583

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 7506	. 2 ⊢ 2𝑜 = suc 1𝑜
2		bj-1ex 32582	. . 3 ⊢ 1𝑜 ∈ V
3	2	sucex 6958	. 2 ⊢ suc 1𝑜 ∈ V
4	1, 3	eqeltri 2694	1 ⊢ 2𝑜 ∈ V

Syntax hints:   ∈ wcel 1987  Vcvv 3186  suc csuc 5684  1_𝑜c1o 7498  2_𝑜c2o 7499

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-8 1989  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pr 4867  ax-un 6902

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rex 2913  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-sn 4149  df-pr 4151  df-uni 4403  df-suc 5688  df-1o 7505  df-2o 7506

This theorem is referenced by: (None)