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

Step	Hyp	Ref	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
4	2, 3	unex 6583	. 2 |- ( f u. { <. n , C >. } ) e. _V
5	1, 4	eqeltri 2527	1 |- G e. _V

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