Description: Values for the group multiple function in a restricted structure. (Contributed by Thierry Arnoux, 12-Jun-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ressmulgnn.1 | |
|
ressmulgnn.2 | |
||
ressmulgnn.3 | |
||
ressmulgnn.4 | |
||
Assertion | ressmulgnn | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressmulgnn.1 | |
|
2 | ressmulgnn.2 | |
|
3 | ressmulgnn.3 | |
|
4 | ressmulgnn.4 | |
|
5 | eqid | |
|
6 | 1 5 | ressbas2 | |
7 | 2 6 | ax-mp | |
8 | eqid | |
|
9 | eqid | |
|
10 | fvex | |
|
11 | 10 2 | ssexi | |
12 | eqid | |
|
13 | 1 12 | ressplusg | |
14 | 11 13 | ax-mp | |
15 | seqeq2 | |
|
16 | 14 15 | ax-mp | |
17 | 7 8 9 16 | mulgnn | |
18 | simpr | |
|
19 | 2 18 | sselid | |
20 | eqid | |
|
21 | 5 12 3 20 | mulgnn | |
22 | 19 21 | syldan | |
23 | 17 22 | eqtr4d | |