Theorem relfsupp 9401

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 9400	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5833	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 395   ∈ wcel 2106  Rel wrel 5694  Fun wfun 6557  (class class class)co 7431   supp csupp 8184  Fincfn 8984   finSupp cfsupp 9399

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-opab 5211  df-xp 5695  df-rel 5696  df-fsupp 9400

This theorem is referenced by:  relprcnfsupp  9402  fsuppimp  9406  suppeqfsuppbi  9417  fsuppsssupp  9419  fsuppss  9421  fsuppssov1  9422  fsuppunbi  9427  funsnfsupp  9430  wemapso2  9591  gsumhashmul  33047