Description: Equivalence between two ways of expressing A as an affine combination of B and C if B and C are not equal. (Contributed by AV, 22-Jan-2023)
Ref | Expression | ||
---|---|---|---|
Hypotheses | affineequiv.a | |
|
affineequiv.b | |
||
affineequiv.c | |
||
affineequiv.d | |
||
affineequivne.d | |
||
Assertion | affineequivne | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | affineequiv.a | |
|
2 | affineequiv.b | |
|
3 | affineequiv.c | |
|
4 | affineequiv.d | |
|
5 | affineequivne.d | |
|
6 | 1 2 3 4 | affineequiv3 | |
7 | 1 2 | subcld | |
8 | 3 2 | subcld | |
9 | 5 | necomd | |
10 | 3 2 9 | subne0d | |
11 | 7 4 8 10 | divmul3d | |
12 | eqcom | |
|
13 | 11 12 | bitr3di | |
14 | 6 13 | bitrd | |