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Theorem bnj918 29573
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 3084 . . 3  |-  f  e. 
_V
3 snex 4659 . . 3  |-  { <. n ,  C >. }  e.  _V
42, 3unex 6600 . 2  |-  ( f  u.  { <. n ,  C >. } )  e. 
_V
51, 4eqeltri 2506 1  |-  G  e. 
_V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437    e. wcel 1868   _Vcvv 3081    u. cun 3434   {csn 3996   <.cop 4002
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-8 1870  ax-9 1872  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400  ax-sep 4543  ax-nul 4552  ax-pr 4657  ax-un 6594
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-rex 2781  df-v 3083  df-dif 3439  df-un 3441  df-nul 3762  df-sn 3997  df-pr 3999  df-uni 4217
This theorem is referenced by:  bnj528  29696  bnj929  29743  bnj965  29749  bnj910  29755  bnj985  29760  bnj999  29764  bnj1018  29769  bnj907  29772
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