Description: The slot for the base set is not the slot for the group operation in an extensible structure. (Contributed by AV, 14-Nov-2021) (Proof shortened by AV, 17-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | basendxnplusgndx | |- ( Base ` ndx ) =/= ( +g ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | basendxnn | |- ( Base ` ndx ) e. NN |
|
| 2 | 1 | nnrei | |- ( Base ` ndx ) e. RR |
| 3 | basendxltplusgndx | |- ( Base ` ndx ) < ( +g ` ndx ) |
|
| 4 | 2 3 | ltneii | |- ( Base ` ndx ) =/= ( +g ` ndx ) |