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Theorem mptrel 5118
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 4499 . 2  |-  ( x  e.  A  |->  B )  =  { <. x ,  y >.  |  ( x  e.  A  /\  y  =  B ) }
21relopabi 5116 1  |-  Rel  (
x  e.  A  |->  B )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 367    = wceq 1398    e. wcel 1823    |-> cmpt 4497   Rel wrel 4993
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-9 1827  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-sep 4560  ax-nul 4568  ax-pr 4676
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-opab 4498  df-mpt 4499  df-xp 4994  df-rel 4995
This theorem is referenced by:  swrd0  12653  dfbigcup2  29780  imageval  29811
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