Theorem bnj918 29577

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 3048	. . 3 |- f e. _V
3		snex 4641	. . 3 |- { <. n , C >. } e. _V
4	2, 3	unex 6589	. 2 |- ( f u. { <. n , C >. } ) e. _V
5	1, 4	eqeltri 2525	1 |- G e. _V

Syntax hints:   = wceq 1444   e. wcel 1887   _Vcvv 3045   u. cun 3402   {csn 3968   <.cop 3974

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-8 1889  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639  ax-un 6583

This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-rex 2743  df-v 3047  df-dif 3407  df-un 3409  df-nul 3732  df-sn 3969  df-pr 3971  df-uni 4199

This theorem is referenced by:  bnj528  29700  bnj929  29747  bnj965  29753  bnj910  29759  bnj985  29764  bnj999  29768  bnj1018  29773  bnj907  29776