Theorem relfsupp 7240

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 7239	. 2 |- finSupp = { <. r , z >. | ( Fun r /\ ( r supp z ) e. Fin ) }
2	1	relopabiv 4878	1 |- Rel finSupp

Syntax hints:   /\ wa 104   e. wcel 2203   Rel wrel 4754   Fun wfun 5346  (class class class)co 6050   supp csupp 6435   Fincfn 6975   finSupp cfsupp 7238

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-v 2815  df-in 3217  df-ss 3224  df-opab 4172  df-xp 4755  df-rel 4756  df-fsupp 7239

This theorem is referenced by:  relprcnfsupp  7241  fsuppimp  7245  suppeqfsuppbi  7248