Theorem relfsupp 9269

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 9268	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5769	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 395   ∈ wcel 2114  Rel wrel 5629  Fun wfun 6486  (class class class)co 7360   supp csupp 8103  Fincfn 8886   finSupp cfsupp 9267

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 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3432  df-ss 3907  df-opab 5149  df-xp 5630  df-rel 5631  df-fsupp 9268

This theorem is referenced by:  relprcnfsupp  9270  fsuppimp  9274  suppeqfsuppbi  9285  fsuppsssupp  9287  fsuppss  9289  fsuppssov1  9290  fsuppunbi  9295  funsnfsupp  9298  wemapso2  9461  gsumhashmul  33143