Theorem reldmmap 8767

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.

Step	Hyp	Ref	Expression
1		df-map 8760	. 2 ⊢ ↑m = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑦⟶𝑥})
2	1	reldmmpo 7488	1 ⊢ Rel dom ↑m

Syntax hints:  {cab 2711  Vcvv 3437  dom cdm 5621  Rel wrel 5626  ⟶wf 6484   ↑_m cmap 8758

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-10 2146  ax-11 2162  ax-12 2182  ax-ext 2705  ax-sep 5238  ax-nul 5248  ax-pr 5374

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2068  df-mo 2537  df-eu 2566  df-clab 2712  df-cleq 2725  df-clel 2808  df-nfc 2882  df-rab 3397  df-v 3439  df-dif 3901  df-un 3903  df-ss 3915  df-nul 4283  df-if 4477  df-sn 4578  df-pr 4580  df-op 4584  df-br 5096  df-opab 5158  df-xp 5627  df-rel 5628  df-dm 5631  df-oprab 7358  df-mpo 7359  df-map 8760

This theorem is referenced by:  mapssfset  8783  mapdom2  9070  efmndbas  18783  smatrcl  33832  mapco2g  42834  naryfvalixp  48757  1aryenef  48773  2aryenef  48784