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 ) ∈ ℕ | |
| 2 | 1 | nnrei | ⊢ ( Base ‘ ndx ) ∈ ℝ |
| 3 | basendxltplusgndx | ⊢ ( Base ‘ ndx ) < ( +g ‘ ndx ) | |
| 4 | 2 3 | ltneii | ⊢ ( Base ‘ ndx ) ≠ ( +g ‘ ndx ) |