Theorem bnj918 32255

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 3414	. . 3 ⊢ 𝑓 ∈ V
3		snex 5298	. . 3 ⊢ {⟨𝑛, 𝐶⟩} ∈ V
4	2, 3	unex 7465	. 2 ⊢ (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
5	1, 4	eqeltri 2849	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1539   ∈ wcel 2112  Vcvv 3410   ∪ cun 3857  {csn 4520  ⟨cop 4526

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2730  ax-sep 5167  ax-nul 5174  ax-pr 5296  ax-un 7457

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 846  df-tru 1542  df-ex 1783  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-v 3412  df-dif 3862  df-un 3864  df-in 3866  df-ss 3876  df-nul 4227  df-sn 4521  df-pr 4523  df-uni 4797

This theorem is referenced by:  bnj528  32379  bnj929  32426  bnj965  32432  bnj910  32438  bnj985v  32443  bnj985  32444  bnj999  32448  bnj1018g  32453  bnj1018  32454  bnj907  32457