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Theorem mptrel 5838
Description: The maps-to notation always describes a binary relation. (Contributed by Scott Fenton, 16-Apr-2012.)
Assertion
Ref Expression
mptrel Rel (𝑥𝐴𝐵)

Proof of Theorem mptrel
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-mpt 5232 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝑦 = 𝐵)}
21relopabiv 5833 1 Rel (𝑥𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wa 395   = wceq 1537  wcel 2106  cmpt 5231  Rel wrel 5694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-opab 5211  df-mpt 5232  df-xp 5695  df-rel 5696
This theorem is referenced by:  fmptco  7149  swrd0  14693  pmtrsn  19552  00lsp  20997  fmptcof2  32674  dfbigcup2  35881  imageval  35912  iscard4  43523
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