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Theorem reldmmap 8860
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 8853 . 2 m = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓𝑓:𝑦𝑥})
21reldmmpo 7561 1 Rel dom ↑m
Colors of variables: wff setvar class
Syntax hints:  {cab 2705  Vcvv 3473  dom cdm 5682  Rel wrel 5687  wf 6549  m cmap 8851
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 2166  ax-ext 2699  ax-sep 5303  ax-nul 5310  ax-pr 5433
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2529  df-eu 2558  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-br 5153  df-opab 5215  df-xp 5688  df-rel 5689  df-dm 5692  df-oprab 7430  df-mpo 7431  df-map 8853
This theorem is referenced by:  mapssfset  8876  mapdom2  9179  efmndbas  18830  smatrcl  33430  mapco2g  42165  naryfvalixp  47780  1aryenef  47796  2aryenef  47807
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