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Theorem bj-0nel1 36324
Description: The empty set does not belong to {1o}. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-0nel1 ∅ ∉ {1o}

Proof of Theorem bj-0nel1
StepHypRef Expression
1 1n0 8483 . . . 4 1o ≠ ∅
21nesymi 2990 . . 3 ¬ ∅ = 1o
3 0ex 5297 . . . 4 ∅ ∈ V
43elsn 4635 . . 3 (∅ ∈ {1o} ↔ ∅ = 1o)
52, 4mtbir 323 . 2 ¬ ∅ ∈ {1o}
65nelir 3041 1 ∅ ∉ {1o}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  wnel 3038  c0 4314  {csn 4620  1oc1o 8454
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 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-nul 5296
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-nel 3039  df-v 3468  df-dif 3943  df-un 3945  df-nul 4315  df-sn 4621  df-suc 6360  df-1o 8461
This theorem is referenced by: (None)
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