Description: Obsolete version of basendxnplusgndx as of 17-Oct-2024. 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 modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | basendxnplusgndxOLD | ⊢ ( Base ‘ ndx ) ≠ ( +g ‘ ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-base | ⊢ Base = Slot 1 | |
| 2 | 1nn | ⊢ 1 ∈ ℕ | |
| 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 ) |