Theorem bnj918 30836

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

Step	Hyp	Ref	Expression
1		bnj918.1	. 2 |- G = ( f u. { <. n , C >. } )
2		vex 3203	. . 3 |- f e. _V
3		snex 4908	. . 3 |- { <. n , C >. } e. _V
4	2, 3	unex 6956	. 2 |- ( f u. { <. n , C >. } ) e. _V
5	1, 4	eqeltri 2697	1 |- G e. _V

Syntax hints:   = wceq 1483   e. wcel 1990   _Vcvv 3200   u. cun 3572   {csn 4177   <.cop 4183

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pr 4906  ax-un 6949

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rex 2918  df-v 3202  df-dif 3577  df-un 3579  df-nul 3916  df-sn 4178  df-pr 4180  df-uni 4437

This theorem is referenced by:  bnj528  30959  bnj929  31006  bnj965  31012  bnj910  31018  bnj985  31023  bnj999  31027  bnj1018  31032  bnj907  31035