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Theorem bnj918 33557
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 3098 . . 3  |-  f  e. 
_V
3 snex 4678 . . 3  |-  { <. n ,  C >. }  e.  _V
42, 3unex 6583 . 2  |-  ( f  u.  { <. n ,  C >. } )  e. 
_V
51, 4eqeltri 2527 1  |-  G  e. 
_V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1383    e. wcel 1804   _Vcvv 3095    u. cun 3459   {csn 4014   <.cop 4020
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-8 1806  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676  ax-un 6577
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-rex 2799  df-v 3097  df-dif 3464  df-un 3466  df-nul 3771  df-sn 4015  df-pr 4017  df-uni 4235
This theorem is referenced by:  bnj528  33680  bnj929  33727  bnj965  33733  bnj910  33739  bnj985  33744  bnj999  33748  bnj1018  33753  bnj907  33756
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