Theorem bnj918 34749

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 3448	. . 3 ⊢ 𝑓 ∈ V
3		snex 5386	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7700	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2824	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1540   ∈ wcel 2109  Vcvv 3444   ∪ cun 3909  {csn 4585  ⟨cop 4591

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-sep 5246  ax-nul 5256  ax-pr 5382  ax-un 7691

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3446  df-dif 3914  df-un 3916  df-ss 3928  df-nul 4293  df-sn 4586  df-pr 4588  df-uni 4868

This theorem is referenced by:  bnj528  34872  bnj929  34919  bnj965  34925  bnj910  34931  bnj985v  34936  bnj985  34937  bnj999  34941  bnj1018g  34946  bnj1018  34947  bnj907  34950