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Theorem reldmmap 7030
Description: Set exponentiation is a well-behaved binary operator. (Contributed by Stefan O'Rear, 27-Feb-2015.)
Assertion
Ref Expression
reldmmap  |-  Rel  dom  ^m

Proof of Theorem reldmmap
Dummy variables  x  f  y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-map 7023 . 2  |-  ^m  =  ( x  e.  _V ,  y  e.  _V  |->  { f  |  f : y --> x }
)
21reldmmpt2 6184 1  |-  Rel  dom  ^m
Colors of variables: wff set class
Syntax hints:   {cab 2424   _Vcvv 2958   dom cdm 4881   Rel wrel 4886   -->wf 5453    ^m cmap 7021
This theorem is referenced by:  mapdom2  7281  mapco2g  26783
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-xp 4887  df-rel 4888  df-dm 4891  df-oprab 6088  df-mpt2 6089  df-map 7023
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