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Theorem mptrel 5685
 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 5134 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝑦 = 𝐵)}
21relopabi 5682 1 Rel (𝑥𝐴𝐵)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 399   = wceq 1538   ∈ wcel 2115   ↦ cmpt 5133  Rel wrel 5548 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-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-sn 4551  df-pr 4553  df-op 4557  df-opab 5116  df-mpt 5134  df-xp 5549  df-rel 5550 This theorem is referenced by:  fmptco  6880  swrd0  14018  pmtrsn  18645  00lsp  19748  fmptcof2  30408  dfbigcup2  33387  imageval  33418  iscard4  40097
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