Theorem bnj918 35164

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 3458	. . 3 ⊢ 𝑓 ∈ V
3		snex 5409	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7744	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2858	1 ⊢ 𝐺 ∈ V

This proof depends on syntax axioms:   = wceq 1569   ∈ wcel 2142  Vcvv 3454   ∪ cun 3902  {csn 4588  ⟨cop 4594

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734  ax-sep 5256  ax-pr 5403  ax-un 7734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-un 3909  df-ss 3921  df-sn 4589  df-pr 4591  df-uni 4872

This theorem is used by:  bnj528  35286  bnj929  35333  bnj965  35339  bnj910  35345  bnj985v  35350  bnj985  35351  bnj999  35355  bnj1018g  35360  bnj1018  35361  bnj907  35364