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Theorem bnj105 29026
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 6728 . 2  |-  1o  =  { (/) }
2 p0ex 4378 . 2  |-  { (/) }  e.  _V
31, 2eqeltri 2505 1  |-  1o  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   _Vcvv 2948   (/)c0 3620   {csn 3806   1oc1o 6709
This theorem is referenced by:  bnj106  29176  bnj118  29177  bnj121  29178  bnj125  29180  bnj130  29182  bnj153  29188
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-pw 3793  df-sn 3812  df-suc 4579  df-1o 6716
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