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Theorem bj-0nel1 33461
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 7847 . . . 4 1o ≠ ∅
21nesymi 3056 . . 3 ¬ ∅ = 1o
3 0ex 5016 . . . 4 ∅ ∈ V
43elsn 4414 . . 3 (∅ ∈ {1o} ↔ ∅ = 1o)
52, 4mtbir 315 . 2 ¬ ∅ ∈ {1o}
65nelir 3105 1 ∅ ∉ {1o}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1656  wcel 2164  wnel 3102  c0 4146  {csn 4399  1oc1o 7824
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803  ax-nul 5015
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ne 3000  df-nel 3103  df-v 3416  df-dif 3801  df-un 3803  df-nul 4147  df-sn 4400  df-suc 5973  df-1o 7831
This theorem is referenced by: (None)
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