MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  2oexOLD Structured version   Visualization version   GIF version

Theorem 2oexOLD 8437
Description: Obsolete version of 2oex 8427 as of 19-Sep-2024. (Contributed by BJ, 6-Apr-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
2oexOLD 2o ∈ V

Proof of Theorem 2oexOLD
StepHypRef Expression
1 df-2o 8417 . 2 2o = suc 1o
2 1oex 8426 . . 3 1o ∈ V
32sucex 7745 . 2 suc 1o ∈ V
41, 3eqeltri 2830 1 2o ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3447  suc csuc 6323  1oc1o 8409  2oc2o 8410
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 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5260  ax-nul 5267  ax-pr 5388  ax-un 7676
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-sn 4591  df-pr 4593  df-uni 4870  df-suc 6327  df-1o 8416  df-2o 8417
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator