Theorem relfsupp 9108

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 9107	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5729	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 396   ∈ wcel 2110  Rel wrel 5595  Fun wfun 6426  (class class class)co 7271   supp csupp 7968  Fincfn 8716   finSupp cfsupp 9106

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 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1545  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-v 3433  df-in 3899  df-ss 3909  df-opab 5142  df-xp 5596  df-rel 5597  df-fsupp 9107

This theorem is referenced by:  relprcnfsupp  9109  fsuppimp  9112  suppeqfsuppbi  9120  fsuppsssupp  9122  fsuppunbi  9127  funsnfsupp  9130  wemapso2  9290  gsumhashmul  31312