Step |
Hyp |
Ref |
Expression |
1 |
|
lmhmpropd.a |
|
2 |
|
lmhmpropd.b |
|
3 |
|
lmhmpropd.c |
|
4 |
|
lmhmpropd.d |
|
5 |
|
lmhmpropd.1 |
|
6 |
|
lmhmpropd.2 |
|
7 |
|
lmhmpropd.3 |
|
8 |
|
lmhmpropd.4 |
|
9 |
|
lmhmpropd.p |
|
10 |
|
lmhmpropd.q |
|
11 |
|
lmhmpropd.e |
|
12 |
|
lmhmpropd.f |
|
13 |
|
lmhmpropd.g |
|
14 |
|
lmhmpropd.h |
|
15 |
1 3 11 5 7 9 13
|
lmodpropd |
|
16 |
2 4 12 6 8 10 14
|
lmodpropd |
|
17 |
15 16
|
anbi12d |
|
18 |
13
|
oveqrspc2v |
|
19 |
18
|
adantlr |
|
20 |
19
|
fveq2d |
|
21 |
|
simpll |
|
22 |
|
simprl |
|
23 |
|
simplrr |
|
24 |
23
|
fveq2d |
|
25 |
24 10 9
|
3eqtr4g |
|
26 |
22 25
|
eleqtrrd |
|
27 |
|
simplrl |
|
28 |
|
eqid |
|
29 |
|
eqid |
|
30 |
28 29
|
ghmf |
|
31 |
27 30
|
syl |
|
32 |
|
simprr |
|
33 |
21 1
|
syl |
|
34 |
32 33
|
eleqtrd |
|
35 |
31 34
|
ffvelrnd |
|
36 |
21 2
|
syl |
|
37 |
35 36
|
eleqtrrd |
|
38 |
14
|
oveqrspc2v |
|
39 |
21 26 37 38
|
syl12anc |
|
40 |
20 39
|
eqeq12d |
|
41 |
40
|
2ralbidva |
|
42 |
41
|
pm5.32da |
|
43 |
|
df-3an |
|
44 |
|
df-3an |
|
45 |
42 43 44
|
3bitr4g |
|
46 |
6 5
|
eqeq12d |
|
47 |
5
|
fveq2d |
|
48 |
9 47
|
syl5eq |
|
49 |
1
|
raleqdv |
|
50 |
48 49
|
raleqbidv |
|
51 |
46 50
|
3anbi23d |
|
52 |
1 2 3 4 11 12
|
ghmpropd |
|
53 |
52
|
eleq2d |
|
54 |
8 7
|
eqeq12d |
|
55 |
7
|
fveq2d |
|
56 |
9 55
|
syl5eq |
|
57 |
3
|
raleqdv |
|
58 |
56 57
|
raleqbidv |
|
59 |
53 54 58
|
3anbi123d |
|
60 |
45 51 59
|
3bitr3d |
|
61 |
17 60
|
anbi12d |
|
62 |
|
eqid |
|
63 |
|
eqid |
|
64 |
|
eqid |
|
65 |
|
eqid |
|
66 |
|
eqid |
|
67 |
62 63 64 28 65 66
|
islmhm |
|
68 |
|
eqid |
|
69 |
|
eqid |
|
70 |
|
eqid |
|
71 |
|
eqid |
|
72 |
|
eqid |
|
73 |
|
eqid |
|
74 |
68 69 70 71 72 73
|
islmhm |
|
75 |
61 67 74
|
3bitr4g |
|
76 |
75
|
eqrdv |
|