Description: 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)
Ref | Expression | ||
---|---|---|---|
Assertion | basendxnmulrndx | ⊢ ( 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 ) |