Theorem bnj918 31646

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 2970	. . 3 |- f e. _V
3		snex 4528	. . 3 |- { <. n , C >. } e. _V
4	2, 3	unex 6373	. 2 |- ( f u. { <. n , C >. } ) e. _V
5	1, 4	eqeltri 2508	1 |- G e. _V

Syntax hints:   = wceq 1369   e. wcel 1756   _Vcvv 2967   u. cun 3321   {csn 3872   <.cop 3878

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-8 1758  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419  ax-sep 4408  ax-nul 4416  ax-pr 4526  ax-un 6367

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rex 2716  df-v 2969  df-dif 3326  df-un 3328  df-nul 3633  df-sn 3873  df-pr 3875  df-uni 4087

This theorem is referenced by:  bnj528  31769  bnj929  31816  bnj965  31822  bnj910  31828  bnj985  31833  bnj999  31837  bnj1018  31842  bnj907  31845