Description: The direct product of a collection of direct products. (Contributed by Mario Carneiro, 25-Apr-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dprd2d.1 | |
|
dprd2d.2 | |
||
dprd2d.3 | |
||
dprd2d.4 | |
||
dprd2d.5 | |
||
dprd2d.k | |
||
Assertion | dprd2db | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dprd2d.1 | |
|
2 | dprd2d.2 | |
|
3 | dprd2d.3 | |
|
4 | dprd2d.4 | |
|
5 | dprd2d.5 | |
|
6 | dprd2d.k | |
|
7 | 1 2 3 4 5 6 | dprd2da | |
8 | 6 | dprdspan | |
9 | 7 8 | syl | |
10 | relssres | |
|
11 | 1 3 10 | syl2anc | |
12 | 11 | imaeq2d | |
13 | ffn | |
|
14 | fnima | |
|
15 | 2 13 14 | 3syl | |
16 | 12 15 | eqtr2d | |
17 | 16 | unieqd | |
18 | 17 | fveq2d | |
19 | ssidd | |
|
20 | 1 2 3 4 5 6 19 | dprd2dlem1 | |
21 | 9 18 20 | 3eqtrd | |