Theorem relfsupp 9321

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 9320	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5786	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 395   ∈ wcel 2109  Rel wrel 5646  Fun wfun 6508  (class class class)co 7390   supp csupp 8142  Fincfn 8921   finSupp cfsupp 9319

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-ss 3934  df-opab 5173  df-xp 5647  df-rel 5648  df-fsupp 9320

This theorem is referenced by:  relprcnfsupp  9322  fsuppimp  9326  suppeqfsuppbi  9337  fsuppsssupp  9339  fsuppss  9341  fsuppssov1  9342  fsuppunbi  9347  funsnfsupp  9350  wemapso2  9513  gsumhashmul  33008