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Theorem bnj918 31352
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 3389 . . 3 𝑓 ∈ V
3 snex 5100 . . 3 {⟨𝑛, 𝐶⟩} ∈ V
42, 3unex 7191 . 2 (𝑓 ∪ {⟨𝑛, 𝐶⟩}) ∈ V
51, 4eqeltri 2875 1 𝐺 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1653  wcel 2157  Vcvv 3386  cun 3768  {csn 4369  cop 4375
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-8 2159  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2378  ax-ext 2778  ax-sep 4976  ax-nul 4984  ax-pr 5098  ax-un 7184
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2787  df-cleq 2793  df-clel 2796  df-nfc 2931  df-rex 3096  df-v 3388  df-dif 3773  df-un 3775  df-nul 4117  df-sn 4370  df-pr 4372  df-uni 4630
This theorem is referenced by:  bnj528  31475  bnj929  31522  bnj965  31528  bnj910  31534  bnj985  31539  bnj999  31543  bnj1018  31548  bnj907  31551
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