Theorem bnj918 34756

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 3451	. . 3 ⊢ 𝑓 ∈ V
3		snex 5391	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7720	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2824	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1540   ∈ wcel 2109  Vcvv 3447   ∪ cun 3912  {csn 4589  ⟨cop 4595

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-sep 5251  ax-nul 5261  ax-pr 5387  ax-un 7711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-dif 3917  df-un 3919  df-ss 3931  df-nul 4297  df-sn 4590  df-pr 4592  df-uni 4872

This theorem is referenced by:  bnj528  34879  bnj929  34926  bnj965  34932  bnj910  34938  bnj985v  34943  bnj985  34944  bnj999  34948  bnj1018g  34953  bnj1018  34954  bnj907  34957