Theorem bnj918 35263

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 3457	. . 3 ⊢ 𝑓 ∈ V
3		snex 5408	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7749	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2858	1 ⊢ 𝐺 ∈ V

This proof depends on syntax axioms:   = wceq 1570   ∈ wcel 2145  Vcvv 3453   ∪ cun 3900  {csn 4587  ⟨cop 4593

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734  ax-sep 5255  ax-pr 5402  ax-un 7739

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3455  df-un 3907  df-ss 3919  df-sn 4588  df-pr 4590  df-uni 4871

This theorem is used by:  bnj528  35385  bnj929  35432  bnj965  35438  bnj910  35444  bnj985v  35449  bnj985  35450  bnj999  35454  bnj1018g  35459  bnj1018  35460  bnj907  35463