Theorem bnj918 34901

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 3443	. . 3 ⊢ 𝑓 ∈ V
3		snex 5380	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7689	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2831	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1542   ∈ wcel 2114  Vcvv 3439   ∪ cun 3898  {csn 4579  ⟨cop 4585

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2707  ax-sep 5240  ax-nul 5250  ax-pr 5376  ax-un 7680

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2714  df-cleq 2727  df-clel 2810  df-v 3441  df-dif 3903  df-un 3905  df-ss 3917  df-nul 4285  df-sn 4580  df-pr 4582  df-uni 4863

This theorem is referenced by:  bnj528  35024  bnj929  35071  bnj965  35077  bnj910  35083  bnj985v  35088  bnj985  35089  bnj999  35093  bnj1018g  35098  bnj1018  35099  bnj907  35102