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Theorem bj-1nel0 35131
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 8307 . . . 4 1o ≠ ∅
21neii 2945 . . 3 ¬ 1o = ∅
3 elsni 4580 . . 3 (1o ∈ {∅} → 1o = ∅)
42, 3mto 196 . 2 ¬ 1o ∈ {∅}
54nelir 3052 1 1o ∉ {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  wcel 2106  wnel 3049  c0 4258  {csn 4563  1oc1o 8279
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709  ax-nul 5230
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-ne 2944  df-nel 3050  df-v 3433  df-dif 3891  df-un 3893  df-nul 4259  df-sn 4564  df-suc 6267  df-1o 8286
This theorem is referenced by: (None)
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