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Theorem bnj105 34124
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 7060 . 2  |-  1o  =  { (/) }
2 p0ex 4552 . 2  |-  { (/) }  e.  _V
31, 2eqeltri 2466 1  |-  1o  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1826   _Vcvv 3034   (/)c0 3711   {csn 3944   1oc1o 7041
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-9 1830  ax-10 1845  ax-11 1850  ax-12 1862  ax-13 2006  ax-ext 2360  ax-sep 4488  ax-nul 4496  ax-pow 4543
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1402  df-ex 1621  df-nf 1625  df-sb 1748  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2532  df-ne 2579  df-v 3036  df-dif 3392  df-un 3394  df-in 3396  df-ss 3403  df-nul 3712  df-pw 3929  df-sn 3945  df-suc 4798  df-1o 7048
This theorem is referenced by:  bnj106  34273  bnj118  34274  bnj121  34275  bnj125  34277  bnj130  34279  bnj153  34285
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