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Theorem ex-br 30450
Description: Example for df-br 5144. 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 5469 . . . 4 ⟨3, 9⟩ ∈ V
21prid2 4763 . . 3 ⟨3, 9⟩ ∈ {⟨2, 6⟩, ⟨3, 9⟩}
3 id 22 . . 3 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 𝑅 = {⟨2, 6⟩, ⟨3, 9⟩})
42, 3eleqtrrid 2848 . 2 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → ⟨3, 9⟩ ∈ 𝑅)
5 df-br 5144 . 2 (3𝑅9 ↔ ⟨3, 9⟩ ∈ 𝑅)
64, 5sylibr 234 1 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 3𝑅9)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  wcel 2108  {cpr 4628  cop 4632   class class class wbr 5143  2c2 12321  3c3 12322  6c6 12325  9c9 12328
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-br 5144
This theorem is referenced by: (None)
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