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Theorem bnj105 32051
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj105 1o ∈ V

Proof of Theorem bnj105
StepHypRef Expression
1 df1o2 8112 . 2 1o = {∅}
2 p0ex 5272 . 2 {∅} ∈ V
31, 2eqeltri 2912 1 1o ∈ V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2115  Vcvv 3480  ∅c0 4276  {csn 4550  1oc1o 8091 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pow 5253 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-pw 4524  df-sn 4551  df-suc 6184  df-1o 8098 This theorem is referenced by:  bnj106  32197  bnj118  32198  bnj121  32199  bnj125  32201  bnj130  32203  bnj153  32209
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