Theorem bnj918 32646

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 3426	. . 3 ⊢ 𝑓 ∈ V
3		snex 5349	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7574	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2835	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1539   ∈ wcel 2108  Vcvv 3422   ∪ cun 3881  {csn 4558  ⟨cop 4564

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-sep 5218  ax-nul 5225  ax-pr 5347  ax-un 7566

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4254  df-sn 4559  df-pr 4561  df-uni 4837

This theorem is referenced by:  bnj528  32769  bnj929  32816  bnj965  32822  bnj910  32828  bnj985v  32833  bnj985  32834  bnj999  32838  bnj1018g  32843  bnj1018  32844  bnj907  32847