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)
Ref | Expression | ||
---|---|---|---|
Assertion | basendxnplusgndx | |- ( Base ` ndx ) =/= ( +g ` ndx ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-base | |- Base = Slot 1 |
|
2 | 1nn | |- 1 e. NN |
|
3 | 1 2 | ndxarg | |- ( Base ` ndx ) = 1 |
4 | 1ne2 | |- 1 =/= 2 |
|
5 | plusgndx | |- ( +g ` ndx ) = 2 |
|
6 | 4 5 | neeqtrri | |- 1 =/= ( +g ` ndx ) |
7 | 3 6 | eqnetri | |- ( Base ` ndx ) =/= ( +g ` ndx ) |