Description: The slot for the inner product is not the slot for the ring (multiplication) operation in an extensible structure. Formerly part of proof for mgpsca . (Contributed by AV, 29-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ipndxnmulrndx | |- ( .i ` ndx ) =/= ( .r ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3re | |- 3 e. RR |
|
| 2 | 3lt8 | |- 3 < 8 |
|
| 3 | 1 2 | gtneii | |- 8 =/= 3 |
| 4 | ipndx | |- ( .i ` ndx ) = 8 |
|
| 5 | mulrndx | |- ( .r ` ndx ) = 3 |
|
| 6 | 4 5 | neeq12i | |- ( ( .i ` ndx ) =/= ( .r ` ndx ) <-> 8 =/= 3 ) |
| 7 | 3 6 | mpbir | |- ( .i ` ndx ) =/= ( .r ` ndx ) |