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Theorem bnj105 33205
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 8415 . 2 1o = {∅}
2 p0ex 5337 . 2 {∅} ∈ V
31, 2eqeltri 2834 1 1o ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  Vcvv 3443  c0 4280  {csn 4584  1oc1o 8401
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-sep 5254  ax-nul 5261  ax-pow 5318
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3445  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4281  df-pw 4560  df-sn 4585  df-suc 6321  df-1o 8408
This theorem is referenced by:  bnj106  33349  bnj118  33350  bnj121  33351  bnj125  33353  bnj130  33355  bnj153  33361
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