Description: The slot for the base set is not the slot for the ring (multiplication) operation in an extensible structure. (Contributed by AV, 16-Feb-2020) (Proof shortened by AV, 28-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | basendxnmulrndx | |- ( Base ` ndx ) =/= ( .r ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | basendx | |- ( Base ` ndx ) = 1 |
|
| 2 | 1re | |- 1 e. RR |
|
| 3 | 1lt3 | |- 1 < 3 |
|
| 4 | 2 3 | ltneii | |- 1 =/= 3 |
| 5 | mulrndx | |- ( .r ` ndx ) = 3 |
|
| 6 | 4 5 | neeqtrri | |- 1 =/= ( .r ` ndx ) |
| 7 | 1 6 | eqnetri | |- ( Base ` ndx ) =/= ( .r ` ndx ) |