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Theorem ex-br 30179
Description: Example for df-br 5140. 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 5455 . . . 4 ⟨3, 9⟩ ∈ V
21prid2 4760 . . 3 ⟨3, 9⟩ ∈ {⟨2, 6⟩, ⟨3, 9⟩}
3 id 22 . . 3 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 𝑅 = {⟨2, 6⟩, ⟨3, 9⟩})
42, 3eleqtrrid 2832 . 2 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → ⟨3, 9⟩ ∈ 𝑅)
5 df-br 5140 . 2 (3𝑅9 ↔ ⟨3, 9⟩ ∈ 𝑅)
64, 5sylibr 233 1 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 3𝑅9)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wcel 2098  {cpr 4623  cop 4627   class class class wbr 5139  2c2 12266  3c3 12267  6c6 12270  9c9 12273
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 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-br 5140
This theorem is referenced by: (None)
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