Theorem relfsupp 9258

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 9257	. 2 ⊢ finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
2	1	relopabiv 5766	1 ⊢ Rel finSupp

Syntax hints:   ∧ wa 395   ∈ wcel 2113  Rel wrel 5626  Fun wfun 6483  (class class class)co 7355   supp csupp 8099  Fincfn 8879   finSupp cfsupp 9256

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 2115  ax-9 2123  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-v 3439  df-ss 3915  df-opab 5158  df-xp 5627  df-rel 5628  df-fsupp 9257

This theorem is referenced by:  relprcnfsupp  9259  fsuppimp  9263  suppeqfsuppbi  9274  fsuppsssupp  9276  fsuppss  9278  fsuppssov1  9279  fsuppunbi  9284  funsnfsupp  9287  wemapso2  9450  gsumhashmul  33078