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Theorem bnj918 29135
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj918.1  |-  G  =  ( f  u.  { <. n ,  C >. } )
Assertion
Ref Expression
bnj918  |-  G  e. 
_V

Proof of Theorem bnj918
StepHypRef Expression
1 bnj918.1 . 2  |-  G  =  ( f  u.  { <. n ,  C >. } )
2 vex 2959 . . 3  |-  f  e. 
_V
3 snex 4405 . . 3  |-  { <. n ,  C >. }  e.  _V
42, 3unex 4707 . 2  |-  ( f  u.  { <. n ,  C >. } )  e. 
_V
51, 4eqeltri 2506 1  |-  G  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725   _Vcvv 2956    u. cun 3318   {csn 3814   <.cop 3817
This theorem is referenced by:  bnj528  29260  bnj929  29307  bnj965  29313  bnj910  29319  bnj985  29324  bnj999  29328  bnj1018  29333  bnj907  29336
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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403  ax-un 4701
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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-rex 2711  df-v 2958  df-dif 3323  df-un 3325  df-nul 3629  df-sn 3820  df-pr 3821  df-uni 4016
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