Description: Association of the disjointness constraint in a subgroup sum. (Contributed by Mario Carneiro, 21-Apr-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lsmcntz.p | |
|
lsmcntz.s | |
||
lsmcntz.t | |
||
lsmcntz.u | |
||
lsmdisj.o | |
||
lsmdisj3b.z | |
||
lsmdisj3b.2 | |
||
Assertion | lsmdisj3b | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lsmcntz.p | |
|
2 | lsmcntz.s | |
|
3 | lsmcntz.t | |
|
4 | lsmcntz.u | |
|
5 | lsmdisj.o | |
|
6 | lsmdisj3b.z | |
|
7 | lsmdisj3b.2 | |
|
8 | 1 2 4 3 5 | lsmdisj2b | |
9 | 1 6 | lsmcom2 | |
10 | 3 4 7 9 | syl3anc | |
11 | 10 | ineq2d | |
12 | 11 | eqeq1d | |
13 | incom | |
|
14 | 13 | a1i | |
15 | 14 | eqeq1d | |
16 | 12 15 | anbi12d | |
17 | 8 16 | bitr4d | |