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Theorem ex-br 28214
 Description: Example for df-br 5054. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.)
Assertion
Ref Expression
ex-br (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 3𝑅9)

Proof of Theorem ex-br
StepHypRef Expression
1 opex 5344 . . . 4 ⟨3, 9⟩ ∈ V
21prid2 4684 . . 3 ⟨3, 9⟩ ∈ {⟨2, 6⟩, ⟨3, 9⟩}
3 id 22 . . 3 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 𝑅 = {⟨2, 6⟩, ⟨3, 9⟩})
42, 3eleqtrrid 2923 . 2 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → ⟨3, 9⟩ ∈ 𝑅)
5 df-br 5054 . 2 (3𝑅9 ↔ ⟨3, 9⟩ ∈ 𝑅)
64, 5sylibr 237 1 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 3𝑅9)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   ∈ wcel 2115  {cpr 4552  ⟨cop 4556   class class class wbr 5053  2c2 11687  3c3 11688  6c6 11691  9c9 11694 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5190  ax-nul 5197  ax-pr 5318 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-br 5054 This theorem is referenced by: (None)
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