Step |
Hyp |
Ref |
Expression |
1 |
|
rngdi.b |
|
2 |
|
rngdi.p |
|
3 |
|
rngdi.t |
|
4 |
|
eqid |
|
5 |
1 4 2 3
|
isrng |
|
6 |
|
oveq1 |
|
7 |
|
oveq1 |
|
8 |
|
oveq1 |
|
9 |
7 8
|
oveq12d |
|
10 |
6 9
|
eqeq12d |
|
11 |
|
oveq1 |
|
12 |
11
|
oveq1d |
|
13 |
8
|
oveq1d |
|
14 |
12 13
|
eqeq12d |
|
15 |
10 14
|
anbi12d |
|
16 |
|
oveq1 |
|
17 |
16
|
oveq2d |
|
18 |
|
oveq2 |
|
19 |
18
|
oveq1d |
|
20 |
17 19
|
eqeq12d |
|
21 |
|
oveq2 |
|
22 |
21
|
oveq1d |
|
23 |
|
oveq1 |
|
24 |
23
|
oveq2d |
|
25 |
22 24
|
eqeq12d |
|
26 |
20 25
|
anbi12d |
|
27 |
|
oveq2 |
|
28 |
27
|
oveq2d |
|
29 |
|
oveq2 |
|
30 |
29
|
oveq2d |
|
31 |
28 30
|
eqeq12d |
|
32 |
|
oveq2 |
|
33 |
|
oveq2 |
|
34 |
29 33
|
oveq12d |
|
35 |
32 34
|
eqeq12d |
|
36 |
31 35
|
anbi12d |
|
37 |
15 26 36
|
rspc3v |
|
38 |
|
simpr |
|
39 |
37 38
|
syl6com |
|
40 |
39
|
3ad2ant3 |
|
41 |
5 40
|
sylbi |
|
42 |
41
|
imp |
|