Description: .s is unaffected by scalar restriction. (Contributed by Thierry Arnoux, 6-Sep-2018)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | resvbas.1 | |- H = ( G |`v A ) |
|
| resvmulr.2 | |- .x. = ( .r ` G ) |
||
| Assertion | resvmulr | |- ( A e. V -> .x. = ( .r ` H ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | resvbas.1 | |- H = ( G |`v A ) |
|
| 2 | resvmulr.2 | |- .x. = ( .r ` G ) |
|
| 3 | df-mulr | |- .r = Slot 3 |
|
| 4 | 3nn | |- 3 e. NN |
|
| 5 | 3re | |- 3 e. RR |
|
| 6 | 3lt5 | |- 3 < 5 |
|
| 7 | 5 6 | ltneii | |- 3 =/= 5 |
| 8 | 1 2 3 4 7 | resvlem | |- ( A e. V -> .x. = ( .r ` H ) ) |