Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-1ex Structured version   Visualization version   GIF version

Theorem bj-1ex 32913
Description: 1𝑜 is a set. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-1ex 1𝑜 ∈ V

Proof of Theorem bj-1ex
StepHypRef Expression
1 df-1o 7545 . 2 1𝑜 = suc ∅
2 0ex 4781 . . 3 ∅ ∈ V
32sucex 6996 . 2 suc ∅ ∈ V
41, 3eqeltri 2695 1 1𝑜 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 1988  Vcvv 3195  c0 3907  suc csuc 5713  1𝑜c1o 7538
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-8 1990  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600  ax-sep 4772  ax-nul 4780  ax-pr 4897  ax-un 6934
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-rex 2915  df-v 3197  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-sn 4169  df-pr 4171  df-uni 4428  df-suc 5717  df-1o 7545
This theorem is referenced by:  bj-2ex  32914  bj-pr2val  32981  bj-2upln1upl  32987
  Copyright terms: Public domain W3C validator