Metamath Proof Explorer


Theorem resvvsca

Description: .s is unaffected by scalar restriction. (Contributed by Thierry Arnoux, 6-Sep-2018) (Proof shortened by AV, 31-Oct-2024)

Ref Expression
Hypotheses resvbas.1 H=G𝑣A
resvvsca.2 ·˙=G
Assertion resvvsca AV·˙=H

Proof

Step Hyp Ref Expression
1 resvbas.1 H=G𝑣A
2 resvvsca.2 ·˙=G
3 vscaid 𝑠=Slotndx
4 vscandxnscandx ndxScalarndx
5 1 2 3 4 resvlem AV·˙=H