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Theorem mptrel 5827
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 5822 1 Rel (𝑥𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wa 395   = wceq 1534  wcel 2099  cmpt 5231  Rel wrel 5683
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-in 3954  df-ss 3964  df-opab 5211  df-mpt 5232  df-xp 5684  df-rel 5685
This theorem is referenced by:  fmptco  7138  swrd0  14641  pmtrsn  19474  00lsp  20865  fmptcof2  32456  dfbigcup2  35495  imageval  35526  iscard4  42963
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