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Theorem bnj918 30090
 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
StepHypRef Expression
1 bnj918.1 . 2 𝐺 = (𝑓 ∪ {⟨𝑛, 𝐶⟩})
2 vex 3176 . . 3 𝑓 ∈ V
3 snex 4835 . . 3 {⟨𝑛, 𝐶⟩} ∈ V
42, 3unex 6854 . 2 (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
51, 4eqeltri 2684 1 𝐺 ∈ V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∈ wcel 1977  Vcvv 3173   ∪ cun 3538  {csn 4125  ⟨cop 4131 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833  ax-un 6847 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-v 3175  df-dif 3543  df-un 3545  df-nul 3875  df-sn 4126  df-pr 4128  df-uni 4373 This theorem is referenced by:  bnj528  30213  bnj929  30260  bnj965  30266  bnj910  30272  bnj985  30277  bnj999  30281  bnj1018  30286  bnj907  30289
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