Description: The function S is a family having trivial intersections. (Contributed by Mario Carneiro, 25-Apr-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dprdcntz.1 | |
|
dprdcntz.2 | |
||
dprdcntz.3 | |
||
dprddisj.0 | |
||
dprddisj.k | |
||
Assertion | dprddisj | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dprdcntz.1 | |
|
2 | dprdcntz.2 | |
|
3 | dprdcntz.3 | |
|
4 | dprddisj.0 | |
|
5 | dprddisj.k | |
|
6 | fveq2 | |
|
7 | sneq | |
|
8 | 7 | difeq2d | |
9 | 8 | imaeq2d | |
10 | 9 | unieqd | |
11 | 10 | fveq2d | |
12 | 6 11 | ineq12d | |
13 | 12 | eqeq1d | |
14 | 1 2 | dprddomcld | |
15 | eqid | |
|
16 | 15 4 5 | dmdprd | |
17 | 14 2 16 | syl2anc | |
18 | 1 17 | mpbid | |
19 | 18 | simp3d | |
20 | simpr | |
|
21 | 20 | ralimi | |
22 | 19 21 | syl | |
23 | 13 22 3 | rspcdva | |