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Theorem reldmmap 8824
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 8817 . 2 m = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓𝑓:𝑦𝑥})
21reldmmpo 7537 1 Rel dom ↑m
Colors of variables: wff setvar class
Syntax hints:  {cab 2710  Vcvv 3475  dom cdm 5674  Rel wrel 5679  wf 6535  m cmap 8815
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5297  ax-nul 5304  ax-pr 5425
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-eu 2564  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-rab 3434  df-v 3477  df-dif 3949  df-un 3951  df-in 3953  df-ss 3963  df-nul 4321  df-if 4527  df-sn 4627  df-pr 4629  df-op 4633  df-br 5147  df-opab 5209  df-xp 5680  df-rel 5681  df-dm 5684  df-oprab 7407  df-mpo 7408  df-map 8817
This theorem is referenced by:  mapssfset  8840  mapdom2  9143  efmndbas  18747  smatrcl  32713  mapco2g  41384  naryfvalixp  47216  1aryenef  47232  2aryenef  47243
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