Description: The slot for the order is not the slot for the base set in an extensible structure. (Contributed by AV, 21-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | plendxnbasendx | |- ( le ` ndx ) =/= ( Base ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1re | |- 1 e. RR |
|
| 2 | 1lt10 | |- 1 < ; 1 0 |
|
| 3 | 1 2 | gtneii | |- ; 1 0 =/= 1 |
| 4 | plendx | |- ( le ` ndx ) = ; 1 0 |
|
| 5 | basendx | |- ( Base ` ndx ) = 1 |
|
| 6 | 4 5 | neeq12i | |- ( ( le ` ndx ) =/= ( Base ` ndx ) <-> ; 1 0 =/= 1 ) |
| 7 | 3 6 | mpbir | |- ( le ` ndx ) =/= ( Base ` ndx ) |