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Theorem bnj918 28307
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 2825 . . 3  |-  f  e. 
_V
3 snex 4253 . . 3  |-  { <. n ,  C >. }  e.  _V
42, 3unex 4555 . 2  |-  ( f  u.  { <. n ,  C >. } )  e. 
_V
51, 4eqeltri 2386 1  |-  G  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1633    e. wcel 1701   _Vcvv 2822    u. cun 3184   {csn 3674   <.cop 3677
This theorem is referenced by:  bnj528  28432  bnj929  28479  bnj965  28485  bnj910  28491  bnj985  28496  bnj999  28500  bnj1018  28505  bnj907  28508
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-13 1703  ax-14 1705  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178  ax-nul 4186  ax-pr 4251  ax-un 4549
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ne 2481  df-rex 2583  df-v 2824  df-dif 3189  df-un 3191  df-nul 3490  df-sn 3680  df-pr 3681  df-uni 3865
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