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Mathbox for Thierry Arnoux |
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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 7435. (Contributed by Thierry Arnoux, 6-Sep-2018.) |
Ref | Expression |
---|---|
reldmresv | ⊢ Rel dom ↾v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-resv 32401 | . 2 ⊢ ↾v = (𝑦 ∈ V, 𝑥 ∈ V ↦ if((Base‘(Scalar‘𝑦)) ⊆ 𝑥, 𝑦, (𝑦 sSet 〈(Scalar‘ndx), ((Scalar‘𝑦) ↾s 𝑥)〉))) | |
2 | 1 | reldmmpo 7530 | 1 ⊢ Rel dom ↾v |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3475 ⊆ wss 3946 ifcif 4524 〈cop 4630 dom cdm 5672 Rel wrel 5677 ‘cfv 6535 (class class class)co 7396 sSet csts 17083 ndxcnx 17113 Basecbs 17131 ↾s cress 17160 Scalarcsca 17187 ↾v cresv 32400 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5295 ax-nul 5302 ax-pr 5423 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-rab 3434 df-v 3477 df-dif 3949 df-un 3951 df-in 3953 df-ss 3963 df-nul 4321 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-br 5145 df-opab 5207 df-xp 5678 df-rel 5679 df-dm 5682 df-oprab 7400 df-mpo 7401 df-resv 32401 |
This theorem is referenced by: resvsca 32406 resvlem 32407 resvlemOLD 32408 |
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