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Theorem bnj105 31130
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 7726 . 2 1𝑜 = {∅}
2 p0ex 4984 . 2 {∅} ∈ V
31, 2eqeltri 2846 1 1𝑜 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2145  Vcvv 3351  c0 4063  {csn 4316  1𝑜c1o 7706
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915  ax-nul 4923  ax-pow 4974
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-v 3353  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-pw 4299  df-sn 4317  df-suc 5872  df-1o 7713
This theorem is referenced by:  bnj106  31276  bnj118  31277  bnj121  31278  bnj125  31280  bnj130  31282  bnj153  31288
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