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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 6684. (Contributed by Thierry Arnoux, 6-Sep-2018.) |
Ref | Expression |
---|---|
reldmresv | ⊢ Rel dom ↾v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-resv 29825 | . 2 ⊢ ↾v = (𝑦 ∈ V, 𝑥 ∈ V ↦ if((Base‘(Scalar‘𝑦)) ⊆ 𝑥, 𝑦, (𝑦 sSet 〈(Scalar‘ndx), ((Scalar‘𝑦) ↾s 𝑥)〉))) | |
2 | 1 | reldmmpt2 6771 | 1 ⊢ Rel dom ↾v |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3200 ⊆ wss 3574 ifcif 4086 〈cop 4183 dom cdm 5114 Rel wrel 5119 ‘cfv 5888 (class class class)co 6650 ndxcnx 15854 sSet csts 15855 Basecbs 15857 ↾s cress 15858 Scalarcsca 15944 ↾v cresv 29824 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-dm 5124 df-oprab 6654 df-mpt2 6655 df-resv 29825 |
This theorem is referenced by: resvsca 29830 resvlem 29831 |
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