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Theorem mptrel 5237
Description: The maps-to notation always describes a relationship. (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 4721 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝑦 = 𝐵)}
21relopabi 5234 1 Rel (𝑥𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wa 384   = wceq 1481  wcel 1988  cmpt 4720  Rel wrel 5109
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-rab 2918  df-v 3197  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-if 4078  df-sn 4169  df-pr 4171  df-op 4175  df-opab 4704  df-mpt 4721  df-xp 5110  df-rel 5111
This theorem is referenced by:  fmptco  6382  swrd0  13416  dfbigcup2  31981  imageval  32012
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