Step |
Hyp |
Ref |
Expression |
1 |
|
imassrn |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
2 3
|
mhmf |
|
5 |
4
|
adantr |
|
6 |
5
|
frnd |
|
7 |
1 6
|
sstrid |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
8 9
|
mhm0 |
|
11 |
10
|
adantr |
|
12 |
5
|
ffnd |
|
13 |
2
|
submss |
|
14 |
13
|
adantl |
|
15 |
8
|
subm0cl |
|
16 |
15
|
adantl |
|
17 |
|
fnfvima |
|
18 |
12 14 16 17
|
syl3anc |
|
19 |
11 18
|
eqeltrrd |
|
20 |
|
simpl |
|
21 |
|
eqidd |
|
22 |
|
eqidd |
|
23 |
|
eqid |
|
24 |
23
|
submcl |
|
25 |
24
|
3adant1l |
|
26 |
20 14 21 22 25
|
mhmimalem |
|
27 |
|
mhmrcl2 |
|
28 |
27
|
adantr |
|
29 |
|
eqid |
|
30 |
3 9 29
|
issubm |
|
31 |
28 30
|
syl |
|
32 |
7 19 26 31
|
mpbir3and |
|