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Theorem bnj918 32025
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 3496 . . 3 𝑓 ∈ V
3 snex 5322 . . 3 {⟨𝑛, 𝐶⟩} ∈ V
42, 3unex 7461 . 2 (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
51, 4eqeltri 2907 1 𝐺 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1530  wcel 2107  Vcvv 3493  cun 3932  {csn 4559  cop 4565
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2791  ax-sep 5194  ax-nul 5201  ax-pr 5320  ax-un 7453
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-rex 3142  df-v 3495  df-dif 3937  df-un 3939  df-nul 4290  df-sn 4560  df-pr 4562  df-uni 4831
This theorem is referenced by:  bnj528  32149  bnj929  32196  bnj965  32202  bnj910  32208  bnj985v  32213  bnj985  32214  bnj999  32218  bnj1018g  32223  bnj1018  32224  bnj907  32227
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