Theorem relfsupp 9319

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 9318	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5805	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 400   ∈ wcel 2149  Rel wrel 5664  Fun wfun 6527  (class class class)co 7408   supp csupp 8152  Fincfn 8939   finSupp cfsupp 9317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3465  df-ss 3930  df-opab 5175  df-xp 5665  df-rel 5666  df-fsupp 9318

This theorem is referenced by:  relprcnfsupp  9320  fsuppimp  9324  suppeqfsuppbi  9335  fsuppsssupp  9337  fsuppss  9339  fsuppssov1  9340  fsuppunbi  9345  funsnfsupp  9348  wemapso2  9511  gsumhashmul  33324