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Theorem bj-0nel1 36954
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 8526 . . . 4 1o ≠ ∅
21nesymi 2998 . . 3 ¬ ∅ = 1o
3 0ex 5307 . . . 4 ∅ ∈ V
43elsn 4641 . . 3 (∅ ∈ {1o} ↔ ∅ = 1o)
52, 4mtbir 323 . 2 ¬ ∅ ∈ {1o}
65nelir 3049 1 ∅ ∉ {1o}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wcel 2108  wnel 3046  c0 4333  {csn 4626  1oc1o 8499
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-nul 5306
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-nel 3047  df-v 3482  df-dif 3954  df-un 3956  df-nul 4334  df-sn 4627  df-suc 6390  df-1o 8506
This theorem is referenced by: (None)
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