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Theorem mptrel 5786
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 5194 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝑦 = 𝐵)}
21relopabiv 5781 1 Rel (𝑥𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wa 397   = wceq 1542  wcel 2107  cmpt 5193  Rel wrel 5643
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-in 3922  df-ss 3932  df-opab 5173  df-mpt 5194  df-xp 5644  df-rel 5645
This theorem is referenced by:  fmptco  7080  swrd0  14553  pmtrsn  19308  00lsp  20458  fmptcof2  31615  dfbigcup2  34513  imageval  34544  iscard4  41879
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