Theorem reldmmap 8839

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 8833	. 2 ⊢ ↑m = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑦⟶𝑥})
2	1	reldmmpo 7546	1 ⊢ Rel dom ↑m

This proof depends on syntax axioms:  {cab 2739  Vcvv 3451  dom cdm 5651  Rel wrel 5656  ⟶wf 6527   ↑_m cmap 8831

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-10 2178  ax-11 2194  ax-12 2213  ax-ext 2733  ax-sep 5249  ax-pr 5391

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-nf 1817  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-nfc 2910  df-rab 3414  df-v 3453  df-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4280  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-br 5104  df-opab 5168  df-xp 5657  df-rel 5658  df-dm 5661  df-oprab 7416  df-mpo 7417  df-map 8833

This theorem is used by:  mapssfset  8857  mapdom2  9151  efmndbas  19047  smatrcl  34410  mapco2g  43678  naryfvalixp  49685  1aryenef  49701  2aryenef  49712