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Mirrors > Home > MPE Home > Th. List > Mathboxes > reldmresv | Structured version Visualization version GIF version |
Description: The scalar restriction is a proper operator, so it can be used with ovprc1 7184. (Contributed by Thierry Arnoux, 6-Sep-2018.) |
Ref | Expression |
---|---|
reldmresv | ⊢ Rel dom ↾v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-resv 30825 | . 2 ⊢ ↾v = (𝑦 ∈ V, 𝑥 ∈ V ↦ if((Base‘(Scalar‘𝑦)) ⊆ 𝑥, 𝑦, (𝑦 sSet 〈(Scalar‘ndx), ((Scalar‘𝑦) ↾s 𝑥)〉))) | |
2 | 1 | reldmmpo 7274 | 1 ⊢ Rel dom ↾v |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3492 ⊆ wss 3933 ifcif 4463 〈cop 4563 dom cdm 5548 Rel wrel 5553 ‘cfv 6348 (class class class)co 7145 ndxcnx 16468 sSet csts 16469 Basecbs 16471 ↾s cress 16472 Scalarcsca 16556 ↾v cresv 30824 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pr 5320 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-rab 3144 df-v 3494 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-br 5058 df-opab 5120 df-xp 5554 df-rel 5555 df-dm 5558 df-oprab 7149 df-mpo 7150 df-resv 30825 |
This theorem is referenced by: resvsca 30830 resvlem 30831 |
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