Description: The slot for the uniform set is not the slot for the base set in an extensible structure. (Contributed by AV, 21-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | unifndxnbasendx | |- ( UnifSet ` ndx ) =/= ( Base ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1re | |- 1 e. RR |
|
| 2 | 1nn | |- 1 e. NN |
|
| 3 | 3nn0 | |- 3 e. NN0 |
|
| 4 | 1nn0 | |- 1 e. NN0 |
|
| 5 | 1lt10 | |- 1 < ; 1 0 |
|
| 6 | 2 3 4 5 | declti | |- 1 < ; 1 3 |
| 7 | 1 6 | gtneii | |- ; 1 3 =/= 1 |
| 8 | unifndx | |- ( UnifSet ` ndx ) = ; 1 3 |
|
| 9 | basendx | |- ( Base ` ndx ) = 1 |
|
| 10 | 8 9 | neeq12i | |- ( ( UnifSet ` ndx ) =/= ( Base ` ndx ) <-> ; 1 3 =/= 1 ) |
| 11 | 7 10 | mpbir | |- ( UnifSet ` ndx ) =/= ( Base ` ndx ) |