Theorem bnj918 34744

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 3492	. . 3 ⊢ 𝑓 ∈ V
3		snex 5451	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7781	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2840	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1537   ∈ wcel 2108  Vcvv 3488   ∪ cun 3974  {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 2110  ax-9 2118  ax-ext 2711  ax-sep 5317  ax-nul 5324  ax-pr 5447  ax-un 7772

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 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-sn 4649  df-pr 4651  df-uni 4932

This theorem is referenced by:  bnj528  34867  bnj929  34914  bnj965  34920  bnj910  34926  bnj985v  34931  bnj985  34932  bnj999  34936  bnj1018g  34941  bnj1018  34942  bnj907  34945