Theorem bnj918 34734

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 ∪ {⟨𝑛, 𝐶⟩})

Assertion

Ref	Expression
bnj918	⊢ 𝐺 ∈ V

Proof of Theorem bnj918

Step	Hyp	Ref	Expression
1		bnj918.1	. 2 ⊢ 𝐺 = (𝑓 ∪ {⟨𝑛, 𝐶⟩})
2		vex 3486	. . 3 ⊢ 𝑓 ∈ V
3		snex 5454	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7775	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2834	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1537   ∈ wcel 2103  Vcvv 3482   ∪ cun 3968  {csn 4648  ⟨cop 4654

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2105  ax-9 2113  ax-ext 2705  ax-sep 5320  ax-nul 5327  ax-pr 5450  ax-un 7766

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3484  df-dif 3973  df-un 3975  df-ss 3987  df-nul 4348  df-sn 4649  df-pr 4651  df-uni 4932

This theorem is referenced by:  bnj528  34857  bnj929  34904  bnj965  34910  bnj910  34916  bnj985v  34921  bnj985  34922  bnj999  34926  bnj1018g  34931  bnj1018  34932  bnj907  34935