Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-1nel0 Structured version   Visualization version   GIF version

Theorem bj-1nel0 36139
Description: 1o does not belong to {∅}. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-1nel0 1o ∉ {∅}

Proof of Theorem bj-1nel0
StepHypRef Expression
1 1n0 8492 . . . 4 1o ≠ ∅
21neii 2941 . . 3 ¬ 1o = ∅
3 elsni 4645 . . 3 (1o ∈ {∅} → 1o = ∅)
42, 3mto 196 . 2 ¬ 1o ∈ {∅}
54nelir 3048 1 1o ∉ {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wcel 2105  wnel 3045  c0 4322  {csn 4628  1oc1o 8463
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702  ax-nul 5306
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-ne 2940  df-nel 3046  df-v 3475  df-dif 3951  df-un 3953  df-nul 4323  df-sn 4629  df-suc 6370  df-1o 8470
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator