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Theorem bnj918 29577
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 3048 . . 3  |-  f  e. 
_V
3 snex 4641 . . 3  |-  { <. n ,  C >. }  e.  _V
42, 3unex 6589 . 2  |-  ( f  u.  { <. n ,  C >. } )  e. 
_V
51, 4eqeltri 2525 1  |-  G  e. 
_V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1444    e. wcel 1887   _Vcvv 3045    u. cun 3402   {csn 3968   <.cop 3974
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-8 1889  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639  ax-un 6583
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-rex 2743  df-v 3047  df-dif 3407  df-un 3409  df-nul 3732  df-sn 3969  df-pr 3971  df-uni 4199
This theorem is referenced by:  bnj528  29700  bnj929  29747  bnj965  29753  bnj910  29759  bnj985  29764  bnj999  29768  bnj1018  29773  bnj907  29776
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