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 ) ) |