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Theorem bj-1nel0 34169
 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 8115 . . . 4 1o ≠ ∅
21neii 3023 . . 3 ¬ 1o = ∅
3 elsni 4581 . . 3 (1o ∈ {∅} → 1o = ∅)
42, 3mto 198 . 2 ¬ 1o ∈ {∅}
54nelir 3131 1 1o ∉ {∅}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1530   ∈ wcel 2107   ∉ wnel 3128  ∅c0 4295  {csn 4564  1oc1o 8091 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798  ax-nul 5207 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ne 3022  df-nel 3129  df-v 3502  df-dif 3943  df-un 3945  df-nul 4296  df-sn 4565  df-suc 6196  df-1o 8098 This theorem is referenced by: (None)
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