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Theorem mptrel 25141
Description: The maps-to notation always describes a relationship. (Contributed by Scott Fenton, 16-Apr-2012.)
Assertion
Ref Expression
mptrel  |-  Rel  (
x  e.  A  |->  B )

Proof of Theorem mptrel
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-mpt 4202 . 2  |-  ( x  e.  A  |->  B )  =  { <. x ,  y >.  |  ( x  e.  A  /\  y  =  B ) }
21relopabi 4933 1  |-  Rel  (
x  e.  A  |->  B )
Colors of variables: wff set class
Syntax hints:    /\ wa 359    = wceq 1649    e. wcel 1717    e. cmpt 4200   Rel wrel 4816
This theorem is referenced by:  dfbigcup2  25456  imageval  25486
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pr 4337
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-opab 4201  df-mpt 4202  df-xp 4817  df-rel 4818
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