Theorem bnj918 35125

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 3466	. . 3 ⊢ 𝑓 ∈ V
3		snex 5414	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7746	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2866	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1568   ∈ wcel 2150  Vcvv 3462   ∪ cun 3911  {csn 4594  ⟨cop 4600

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2152  ax-9 2160  ax-ext 2742  ax-sep 5262  ax-pr 5408  ax-un 7736

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1571  df-ex 1808  df-sb 2099  df-clab 2749  df-cleq 2762  df-clel 2845  df-v 3464  df-un 3918  df-ss 3930  df-sn 4595  df-pr 4597  df-uni 4878

This theorem is referenced by:  bnj528  35247  bnj929  35294  bnj965  35300  bnj910  35306  bnj985v  35311  bnj985  35312  bnj999  35316  bnj1018g  35321  bnj1018  35322  bnj907  35325