Step |
Hyp |
Ref |
Expression |
1 |
|
issubrng.b |
|
2 |
|
df-subrng |
|
3 |
2
|
mptrcl |
|
4 |
|
simp1 |
|
5 |
|
fveq2 |
|
6 |
5
|
pweqd |
|
7 |
|
oveq1 |
|
8 |
7
|
eleq1d |
|
9 |
6 8
|
rabeqbidv |
|
10 |
|
df-subrng |
|
11 |
|
fvex |
|
12 |
11
|
pwex |
|
13 |
12
|
rabex |
|
14 |
9 10 13
|
fvmpt |
|
15 |
14
|
eleq2d |
|
16 |
|
oveq2 |
|
17 |
16
|
eleq1d |
|
18 |
17
|
elrab |
|
19 |
1
|
eqcomi |
|
20 |
19
|
sseq2i |
|
21 |
20
|
anbi2i |
|
22 |
|
ibar |
|
23 |
21 22
|
bitrid |
|
24 |
11
|
elpw2 |
|
25 |
24
|
anbi2ci |
|
26 |
|
3anass |
|
27 |
23 25 26
|
3bitr4g |
|
28 |
18 27
|
bitrid |
|
29 |
15 28
|
bitrd |
|
30 |
3 4 29
|
pm5.21nii |
|