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| Description: The property of a function to be finitely supported is a relation. (Contributed by AV, 7-Jun-2019.) | 
| Ref | Expression | 
|---|---|
| relfsupp | ⊢ Rel finSupp | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-fsupp 9403 | . 2 ⊢ finSupp = {〈𝑟, 𝑧〉 ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)} | |
| 2 | 1 | relopabiv 5829 | 1 ⊢ Rel finSupp | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∧ wa 395 ∈ wcel 2107 Rel wrel 5689 Fun wfun 6554 (class class class)co 7432 supp csupp 8186 Fincfn 8986 finSupp cfsupp 9402 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1542 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-ss 3967 df-opab 5205 df-xp 5690 df-rel 5691 df-fsupp 9403 | 
| This theorem is referenced by: relprcnfsupp 9405 fsuppimp 9409 suppeqfsuppbi 9420 fsuppsssupp 9422 fsuppss 9424 fsuppssov1 9425 fsuppunbi 9430 funsnfsupp 9433 wemapso2 9594 gsumhashmul 33065 | 
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