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Theorem mptrel 5818
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 5225 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝑦 = 𝐵)}
21relopabiv 5813 1 Rel (𝑥𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wa 395   = wceq 1533  wcel 2098  cmpt 5224  Rel wrel 5674
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 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-in 3950  df-ss 3960  df-opab 5204  df-mpt 5225  df-xp 5675  df-rel 5676
This theorem is referenced by:  fmptco  7122  swrd0  14612  pmtrsn  19437  00lsp  20826  fmptcof2  32387  dfbigcup2  35404  imageval  35435  iscard4  42841
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