Description: The slot for the scalar is not the slot for the base set in an extensible structure. (Contributed by AV, 21-Oct-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | scandxnbasendx | |- ( Scalar ` ndx ) =/= ( Base ` ndx ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1re | |- 1 e. RR |
|
2 | 1lt5 | |- 1 < 5 |
|
3 | 1 2 | gtneii | |- 5 =/= 1 |
4 | scandx | |- ( Scalar ` ndx ) = 5 |
|
5 | basendx | |- ( Base ` ndx ) = 1 |
|
6 | 4 5 | neeq12i | |- ( ( Scalar ` ndx ) =/= ( Base ` ndx ) <-> 5 =/= 1 ) |
7 | 3 6 | mpbir | |- ( Scalar ` ndx ) =/= ( Base ` ndx ) |