Description: The slot for the "less than or equal to" ordering is not the slot for the scalar product in an extensible structure. Formerly part of proof for opsrvsca . (Contributed by AV, 1-Nov-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | plendxnvscandx | |- ( le ` ndx ) =/= ( .s ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 6re | |- 6 e. RR |
|
| 2 | 6lt10 | |- 6 < ; 1 0 |
|
| 3 | 1 2 | gtneii | |- ; 1 0 =/= 6 |
| 4 | plendx | |- ( le ` ndx ) = ; 1 0 |
|
| 5 | vscandx | |- ( .s ` ndx ) = 6 |
|
| 6 | 4 5 | neeq12i | |- ( ( le ` ndx ) =/= ( .s ` ndx ) <-> ; 1 0 =/= 6 ) |
| 7 | 3 6 | mpbir | |- ( le ` ndx ) =/= ( .s ` ndx ) |