Theorem bnj918 29573

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 3084	. . 3 |- f e. _V
3		snex 4659	. . 3 |- { <. n , C >. } e. _V
4	2, 3	unex 6600	. 2 |- ( f u. { <. n , C >. } ) e. _V
5	1, 4	eqeltri 2506	1 |- G e. _V

Syntax hints:   = wceq 1437   e. wcel 1868   _Vcvv 3081   u. cun 3434   {csn 3996   <.cop 4002

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-8 1870  ax-9 1872  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400  ax-sep 4543  ax-nul 4552  ax-pr 4657  ax-un 6594

This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-rex 2781  df-v 3083  df-dif 3439  df-un 3441  df-nul 3762  df-sn 3997  df-pr 3999  df-uni 4217

This theorem is referenced by:  bnj528  29696  bnj929  29743  bnj965  29749  bnj910  29755  bnj985  29760  bnj999  29764  bnj1018  29769  bnj907  29772