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 ) ∈ ℕ | |
| 2 | 1 | nnrei | ⊢ ( Base ‘ ndx ) ∈ ℝ |
| 3 | basendxltplendx | ⊢ ( Base ‘ ndx ) < ( le ‘ ndx ) | |
| 4 | 2 3 | gtneii | ⊢ ( le ‘ ndx ) ≠ ( Base ‘ ndx ) |