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Theorem bnj105 32030
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj105  |-  1o  e.  _V

Proof of Theorem bnj105
StepHypRef Expression
1 df1o2 7041 . 2  |-  1o  =  { (/) }
2 p0ex 4586 . 2  |-  { (/) }  e.  _V
31, 2eqeltri 2538 1  |-  1o  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758   _Vcvv 3076   (/)c0 3744   {csn 3984   1oc1o 7022
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4520  ax-nul 4528  ax-pow 4577
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2649  df-v 3078  df-dif 3438  df-un 3440  df-in 3442  df-ss 3449  df-nul 3745  df-pw 3969  df-sn 3985  df-suc 4832  df-1o 7029
This theorem is referenced by:  bnj106  32178  bnj118  32179  bnj121  32180  bnj125  32182  bnj130  32184  bnj153  32190
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