![]() |
Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
|
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 7450. (Contributed by Thierry Arnoux, 6-Sep-2018.) |
Ref | Expression |
---|---|
reldmresv | ⊢ Rel dom ↾v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-resv 32709 | . 2 ⊢ ↾v = (𝑦 ∈ V, 𝑥 ∈ V ↦ if((Base‘(Scalar‘𝑦)) ⊆ 𝑥, 𝑦, (𝑦 sSet ⟨(Scalar‘ndx), ((Scalar‘𝑦) ↾s 𝑥)⟩))) | |
2 | 1 | reldmmpo 7545 | 1 ⊢ Rel dom ↾v |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3472 ⊆ wss 3947 ifcif 4527 ⟨cop 4633 dom cdm 5675 Rel wrel 5680 ‘cfv 6542 (class class class)co 7411 sSet csts 17100 ndxcnx 17130 Basecbs 17148 ↾s cress 17177 Scalarcsca 17204 ↾v cresv 32708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5298 ax-nul 5305 ax-pr 5426 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 844 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-rab 3431 df-v 3474 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-sn 4628 df-pr 4630 df-op 4634 df-br 5148 df-opab 5210 df-xp 5681 df-rel 5682 df-dm 5685 df-oprab 7415 df-mpo 7416 df-resv 32709 |
This theorem is referenced by: resvsca 32714 resvlem 32715 resvlemOLD 32716 |
Copyright terms: Public domain | W3C validator |