Theorem relfsupp 8277

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 8276	. 2 |- finSupp = { <. r , z >. | ( Fun r /\ ( r supp z ) e. Fin ) }
2	1	relopabi 5245	1 |- Rel finSupp

Syntax hints:   /\ wa 384   e. wcel 1990   Rel wrel 5119   Fun wfun 5882  (class class class)co 6650   supp csupp 7295   Fincfn 7955   finSupp cfsupp 8275

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-opab 4713  df-xp 5120  df-rel 5121  df-fsupp 8276

This theorem is referenced by:  relprcnfsupp  8278  fsuppimp  8281  suppeqfsuppbi  8289  fsuppsssupp  8291  fsuppunbi  8296  funsnfsupp  8299  wemapso2  8458