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Theorem bj-1nel0 33066
 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 7620 . . . 4 1𝑜 ≠ ∅
21neii 2825 . . 3 ¬ 1𝑜 = ∅
3 elsni 4227 . . 3 (1𝑜 ∈ {∅} → 1𝑜 = ∅)
42, 3mto 188 . 2 ¬ 1𝑜 ∈ {∅}
54nelir 2929 1 1𝑜 ∉ {∅}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1523   ∈ wcel 2030   ∉ wnel 2926  ∅c0 3948  {csn 4210  1𝑜c1o 7598 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-nul 4822 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ne 2824  df-nel 2927  df-v 3233  df-dif 3610  df-un 3612  df-nul 3949  df-sn 4211  df-suc 5767  df-1o 7605 This theorem is referenced by: (None)
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