Theorem bnj918 34764

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 3459	. . 3 ⊢ 𝑓 ∈ V
3		snex 5399	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7727	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2825	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1540   ∈ wcel 2109  Vcvv 3455   ∪ cun 3920  {csn 4597  ⟨cop 4603

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 2702  ax-sep 5259  ax-nul 5269  ax-pr 5395  ax-un 7718

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 2709  df-cleq 2722  df-clel 2804  df-v 3457  df-dif 3925  df-un 3927  df-ss 3939  df-nul 4305  df-sn 4598  df-pr 4600  df-uni 4880

This theorem is referenced by:  bnj528  34887  bnj929  34934  bnj965  34940  bnj910  34946  bnj985v  34951  bnj985  34952  bnj999  34956  bnj1018g  34961  bnj1018  34962  bnj907  34965