Description: +g is unaffected by scalar restriction. (Contributed by Thierry Arnoux, 6-Sep-2018) (Revised by AV, 31-Oct-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | resvbas.1 | |- H = ( G |`v A ) |
|
resvplusg.2 | |- .+ = ( +g ` G ) |
||
Assertion | resvplusg | |- ( A e. V -> .+ = ( +g ` H ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resvbas.1 | |- H = ( G |`v A ) |
|
2 | resvplusg.2 | |- .+ = ( +g ` G ) |
|
3 | plusgid | |- +g = Slot ( +g ` ndx ) |
|
4 | scandxnplusgndx | |- ( Scalar ` ndx ) =/= ( +g ` ndx ) |
|
5 | 4 | necomi | |- ( +g ` ndx ) =/= ( Scalar ` ndx ) |
6 | 1 2 3 5 | resvlem | |- ( A e. V -> .+ = ( +g ` H ) ) |