Theorem relfsupp 9242

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 9241	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5755	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 395   ∈ wcel 2111  Rel wrel 5616  Fun wfun 6470  (class class class)co 7341   supp csupp 8085  Fincfn 8864   finSupp cfsupp 9240

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-ss 3914  df-opab 5149  df-xp 5617  df-rel 5618  df-fsupp 9241

This theorem is referenced by:  relprcnfsupp  9243  fsuppimp  9247  suppeqfsuppbi  9258  fsuppsssupp  9260  fsuppss  9262  fsuppssov1  9263  fsuppunbi  9268  funsnfsupp  9271  wemapso2  9434  gsumhashmul  33033