Theorem relfsupp 9404

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 9403	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5829	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 395   ∈ wcel 2107  Rel wrel 5689  Fun wfun 6554  (class class class)co 7432   supp csupp 8186  Fincfn 8986   finSupp cfsupp 9402

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-ss 3967  df-opab 5205  df-xp 5690  df-rel 5691  df-fsupp 9403

This theorem is referenced by:  relprcnfsupp  9405  fsuppimp  9409  suppeqfsuppbi  9420  fsuppsssupp  9422  fsuppss  9424  fsuppssov1  9425  fsuppunbi  9430  funsnfsupp  9433  wemapso2  9594  gsumhashmul  33065