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Mirrors > Home > MPE Home > Th. List > relfsupp | Structured version Visualization version GIF version |
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 8836 | . 2 ⊢ finSupp = {〈𝑟, 𝑧〉 ∣ (Fun 𝑟 ∧ (𝑟 supp 𝑧) ∈ Fin)} | |
2 | 1 | relopabi 5696 | 1 ⊢ Rel finSupp |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 398 ∈ wcel 2114 Rel wrel 5562 Fun wfun 6351 (class class class)co 7158 supp csupp 7832 Fincfn 8511 finSupp cfsupp 8835 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-opab 5131 df-xp 5563 df-rel 5564 df-fsupp 8836 |
This theorem is referenced by: relprcnfsupp 8838 fsuppimp 8841 suppeqfsuppbi 8849 fsuppsssupp 8851 fsuppunbi 8856 funsnfsupp 8859 wemapso2 9019 |
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