Theorem relfsupp 9276

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 9275	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5776	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 395   ∈ wcel 2114  Rel wrel 5636  Fun wfun 6492  (class class class)co 7367   supp csupp 8110  Fincfn 8893   finSupp cfsupp 9274

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431  df-ss 3906  df-opab 5148  df-xp 5637  df-rel 5638  df-fsupp 9275

This theorem is referenced by:  relprcnfsupp  9277  fsuppimp  9281  suppeqfsuppbi  9292  fsuppsssupp  9294  fsuppss  9296  fsuppssov1  9297  fsuppunbi  9302  funsnfsupp  9305  wemapso2  9468  gsumhashmul  33128