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 = ( G |`v A ) |
|
resvvsca.2 | |- .x. = ( .s ` G ) |
||
Assertion | resvvsca | |- ( A e. V -> .x. = ( .s ` H ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resvbas.1 | |- H = ( G |`v A ) |
|
2 | resvvsca.2 | |- .x. = ( .s ` G ) |
|
3 | vscaid | |- .s = Slot ( .s ` ndx ) |
|
4 | vscandxnscandx | |- ( .s ` ndx ) =/= ( Scalar ` ndx ) |
|
5 | 1 2 3 4 | resvlem | |- ( A e. V -> .x. = ( .s ` H ) ) |