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Theorem relfsupp 8318
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 8317 . 2 finSupp = {⟨𝑟, 𝑧⟩ ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)}
21relopabi 5278 1 Rel finSupp
Colors of variables: wff setvar class
Syntax hints:  wa 383  wcel 2030  Rel wrel 5148  Fun wfun 5920  (class class class)co 6690   supp csupp 7340  Fincfn 7997   finSupp cfsupp 8316
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-opab 4746  df-xp 5149  df-rel 5150  df-fsupp 8317
This theorem is referenced by:  relprcnfsupp  8319  fsuppimp  8322  suppeqfsuppbi  8330  fsuppsssupp  8332  fsuppunbi  8337  funsnfsupp  8340  wemapso2  8499
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