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Theorem bnj918 29896
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 3175 . . 3 𝑓 ∈ V
3 snex 4830 . . 3 {⟨𝑛, 𝐶⟩} ∈ V
42, 3unex 6831 . 2 (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
51, 4eqeltri 2683 1 𝐺 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wcel 1976  Vcvv 3172  cun 3537  {csn 4124  cop 4130
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-8 1978  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703  ax-nul 4712  ax-pr 4828  ax-un 6824
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-rex 2901  df-v 3174  df-dif 3542  df-un 3544  df-nul 3874  df-sn 4125  df-pr 4127  df-uni 4367
This theorem is referenced by:  bnj528  30019  bnj929  30066  bnj965  30072  bnj910  30078  bnj985  30083  bnj999  30087  bnj1018  30092  bnj907  30095
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