Theorem relfsupp 8965

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 8964	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5675	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 399   ∈ wcel 2112  Rel wrel 5541  Fun wfun 6352  (class class class)co 7191   supp csupp 7881  Fincfn 8604   finSupp cfsupp 8963

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-8 2114  ax-9 2122  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2073  df-clab 2715  df-cleq 2728  df-clel 2809  df-v 3400  df-in 3860  df-ss 3870  df-opab 5102  df-xp 5542  df-rel 5543  df-fsupp 8964

This theorem is referenced by:  relprcnfsupp  8966  fsuppimp  8969  suppeqfsuppbi  8977  fsuppsssupp  8979  fsuppunbi  8984  funsnfsupp  8987  wemapso2  9147  gsumhashmul  30989