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 7198. (Contributed by Thierry Arnoux, 6-Sep-2018.) |
Ref | Expression |
---|---|
reldmresv | ⊢ Rel dom ↾v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-resv 30902 | . 2 ⊢ ↾v = (𝑦 ∈ V, 𝑥 ∈ V ↦ if((Base‘(Scalar‘𝑦)) ⊆ 𝑥, 𝑦, (𝑦 sSet 〈(Scalar‘ndx), ((Scalar‘𝑦) ↾s 𝑥)〉))) | |
2 | 1 | reldmmpo 7288 | 1 ⊢ Rel dom ↾v |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3497 ⊆ wss 3939 ifcif 4470 〈cop 4576 dom cdm 5558 Rel wrel 5563 ‘cfv 6358 (class class class)co 7159 ndxcnx 16483 sSet csts 16484 Basecbs 16486 ↾s cress 16487 Scalarcsca 16571 ↾v cresv 30901 |
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 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2796 ax-sep 5206 ax-nul 5213 ax-pr 5333 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-mo 2621 df-eu 2653 df-clab 2803 df-cleq 2817 df-clel 2896 df-nfc 2966 df-rab 3150 df-v 3499 df-dif 3942 df-un 3944 df-in 3946 df-ss 3955 df-nul 4295 df-if 4471 df-sn 4571 df-pr 4573 df-op 4577 df-br 5070 df-opab 5132 df-xp 5564 df-rel 5565 df-dm 5568 df-oprab 7163 df-mpo 7164 df-resv 30902 |
This theorem is referenced by: resvsca 30907 resvlem 30908 |
Copyright terms: Public domain | W3C validator |