Theorem relfsupp 9266

Description: The property of a function to be finitely supported is a relation. (Contributed by AV, 7-Jun-2019.)

Assertion

Ref	Expression
relfsupp	⊢ Rel finSupp

Proof of Theorem relfsupp

Dummy variables 𝑧 𝑟 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-fsupp 9265	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5763	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 396   ∈ wcel 2119  Rel wrel 5623  Fun wfun 6479  (class class class)co 7356   supp csupp 8100  Fincfn 8883   finSupp cfsupp 9264

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-ss 3900  df-opab 5135  df-xp 5624  df-rel 5625  df-fsupp 9265

This theorem is referenced by:  relprcnfsupp  9267  fsuppimp  9271  suppeqfsuppbi  9282  fsuppsssupp  9284  fsuppss  9286  fsuppssov1  9287  fsuppunbi  9292  funsnfsupp  9295  wemapso2  9458  gsumhashmul  33148