Description: The slot for the scalar product is not the slot for the scalar field in an extensible structure. Formerly part of proof for rmodislmod . (Contributed by AV, 18-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | vscandxnscandx | |- ( .s ` ndx ) =/= ( Scalar ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 5re | |- 5 e. RR |
|
| 2 | 5lt6 | |- 5 < 6 |
|
| 3 | 1 2 | gtneii | |- 6 =/= 5 |
| 4 | vscandx | |- ( .s ` ndx ) = 6 |
|
| 5 | scandx | |- ( Scalar ` ndx ) = 5 |
|
| 6 | 4 5 | neeq12i | |- ( ( .s ` ndx ) =/= ( Scalar ` ndx ) <-> 6 =/= 5 ) |
| 7 | 3 6 | mpbir | |- ( .s ` ndx ) =/= ( Scalar ` ndx ) |