Description: Obsolete proof of basendxnmulrndx as of 28-Oct-2024. The slot for the base set is not the slot for the ring (multiplication) operation in an extensible structure. (Contributed by AV, 16-Feb-2020) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | basendxnmulrndxOLD | ⊢ ( Base ‘ ndx ) ≠ ( .r ‘ ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-base | ⊢ Base = Slot 1 | |
| 2 | 1nn | ⊢ 1 ∈ ℕ | |
| 3 | 1 2 | ndxarg | ⊢ ( Base ‘ ndx ) = 1 |
| 4 | 1re | ⊢ 1 ∈ ℝ | |
| 5 | 1lt3 | ⊢ 1 < 3 | |
| 6 | 4 5 | ltneii | ⊢ 1 ≠ 3 |
| 7 | mulrndx | ⊢ ( .r ‘ ndx ) = 3 | |
| 8 | 6 7 | neeqtrri | ⊢ 1 ≠ ( .r ‘ ndx ) |
| 9 | 3 8 | eqnetri | ⊢ ( Base ‘ ndx ) ≠ ( .r ‘ ndx ) |