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Theorem relfsupp 7889
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 7888 . 2  |- finSupp  =  { <. r ,  z >.  |  ( Fun  r  /\  ( r supp  z )  e.  Fin ) }
21relopabi 4976 1  |-  Rel finSupp
Colors of variables: wff setvar class
Syntax hints:    /\ wa 371    e. wcel 1869   Rel wrel 4856   Fun wfun 5593  (class class class)co 6303   supp csupp 6923   Fincfn 7575   finSupp cfsupp 7887
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-9 1873  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401  ax-sep 4544  ax-nul 4553  ax-pr 4658
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ne 2621  df-ral 2781  df-rex 2782  df-rab 2785  df-v 3084  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3763  df-if 3911  df-sn 3998  df-pr 4000  df-op 4004  df-opab 4481  df-xp 4857  df-rel 4858  df-fsupp 7888
This theorem is referenced by:  relprcnfsupp  7890  fsuppimp  7893  suppeqfsuppbi  7901  fsuppsssupp  7903  fsuppunbi  7908  funsnfsupp  7911  wemapso2  8072
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