Theorem relfsupp 9314

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 9313	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5781	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 396   ∈ wcel 2106  Rel wrel 5643  Fun wfun 6495  (class class class)co 7362   supp csupp 8097  Fincfn 8890   finSupp cfsupp 9312

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3448  df-in 3920  df-ss 3930  df-opab 5173  df-xp 5644  df-rel 5645  df-fsupp 9313

This theorem is referenced by:  relprcnfsupp  9315  fsuppimp  9319  suppeqfsuppbi  9328  fsuppsssupp  9330  fsuppunbi  9335  funsnfsupp  9338  wemapso2  9498  gsumhashmul  31968