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Theorem bj-0nel1 34151
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 8113 . . . 4 1o ≠ ∅
21nesymi 3077 . . 3 ¬ ∅ = 1o
3 0ex 5207 . . . 4 ∅ ∈ V
43elsn 4578 . . 3 (∅ ∈ {1o} ↔ ∅ = 1o)
52, 4mtbir 324 . 2 ¬ ∅ ∈ {1o}
65nelir 3130 1 ∅ ∉ {1o}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1530  wcel 2107  wnel 3127  c0 4294  {csn 4563  1oc1o 8089
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 2797  ax-nul 5206
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 2804  df-cleq 2818  df-clel 2897  df-nfc 2967  df-ne 3021  df-nel 3128  df-v 3501  df-dif 3942  df-un 3944  df-nul 4295  df-sn 4564  df-suc 6194  df-1o 8096
This theorem is referenced by: (None)
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