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Theorem reldmmap 8831
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 8824 . 2 m = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓𝑓:𝑦𝑥})
21reldmmpo 7539 1 Rel dom ↑m
Colors of variables: wff setvar class
Syntax hints:  {cab 2703  Vcvv 3468  dom cdm 5669  Rel wrel 5674  wf 6533  m cmap 8822
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2528  df-eu 2557  df-clab 2704  df-cleq 2718  df-clel 2804  df-nfc 2879  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-br 5142  df-opab 5204  df-xp 5675  df-rel 5676  df-dm 5679  df-oprab 7409  df-mpo 7410  df-map 8824
This theorem is referenced by:  mapssfset  8847  mapdom2  9150  efmndbas  18796  smatrcl  33306  mapco2g  42027  naryfvalixp  47587  1aryenef  47603  2aryenef  47614
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