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Theorem relfsupp 8431
 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.
StepHypRef Expression
1 df-fsupp 8430 . 2 finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
21relopabi 5383 1 Rel finSupp
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 383   ∈ wcel 2143  Rel wrel 5253  Fun wfun 6024  (class class class)co 6791   supp csupp 7444  Fincfn 8107   finSupp cfsupp 8429 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1868  ax-4 1883  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2152  ax-10 2172  ax-11 2188  ax-12 2201  ax-13 2406  ax-ext 2749 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1071  df-tru 1632  df-ex 1851  df-nf 1856  df-sb 2048  df-clab 2756  df-cleq 2762  df-clel 2765  df-nfc 2900  df-rab 3068  df-v 3350  df-dif 3723  df-un 3725  df-in 3727  df-ss 3734  df-nul 4061  df-if 4223  df-sn 4314  df-pr 4316  df-op 4320  df-opab 4844  df-xp 5254  df-rel 5255  df-fsupp 8430 This theorem is referenced by:  relprcnfsupp  8432  fsuppimp  8435  suppeqfsuppbi  8443  fsuppsssupp  8445  fsuppunbi  8450  funsnfsupp  8453  wemapso2  8612
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