Description: The slot for the order is not the slot for the base set in an extensible structure. (Contributed by AV, 21-Oct-2024) (Proof shortened by AV, 30-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | plendxnbasendx | |- ( le ` ndx ) =/= ( Base ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | basendxnn | |- ( Base ` ndx ) e. NN |
|
| 2 | 1 | nnrei | |- ( Base ` ndx ) e. RR |
| 3 | basendxltplendx | |- ( Base ` ndx ) < ( le ` ndx ) |
|
| 4 | 2 3 | gtneii | |- ( le ` ndx ) =/= ( Base ` ndx ) |