Step |
Hyp |
Ref |
Expression |
1 |
|
lmhmfgsplit.z |
|
2 |
|
lmhmfgsplit.k |
|
3 |
|
lmhmfgsplit.u |
|
4 |
|
lmhmfgsplit.v |
|
5 |
|
simp3 |
|
6 |
|
lmhmlmod2 |
|
7 |
6
|
3ad2ant1 |
|
8 |
|
lmhmrnlss |
|
9 |
8
|
3ad2ant1 |
|
10 |
|
eqid |
|
11 |
|
eqid |
|
12 |
4 10 11
|
islssfg |
|
13 |
7 9 12
|
syl2anc |
|
14 |
5 13
|
mpbid |
|
15 |
|
simpl1 |
|
16 |
|
eqid |
|
17 |
|
eqid |
|
18 |
16 17
|
lmhmf |
|
19 |
|
ffn |
|
20 |
15 18 19
|
3syl |
|
21 |
|
elpwi |
|
22 |
21
|
ad2antrl |
|
23 |
|
simprrl |
|
24 |
|
fipreima |
|
25 |
20 22 23 24
|
syl3anc |
|
26 |
|
eqid |
|
27 |
|
eqid |
|
28 |
|
simpll1 |
|
29 |
|
lmhmlmod1 |
|
30 |
29
|
3ad2ant1 |
|
31 |
30
|
ad2antrr |
|
32 |
|
inss1 |
|
33 |
32
|
sseli |
|
34 |
|
elpwi |
|
35 |
33 34
|
syl |
|
36 |
35
|
ad2antrl |
|
37 |
|
eqid |
|
38 |
16 26 37
|
lspcl |
|
39 |
31 36 38
|
syl2anc |
|
40 |
16 37 11
|
lmhmlsp |
|
41 |
28 36 40
|
syl2anc |
|
42 |
|
fveq2 |
|
43 |
42
|
ad2antll |
|
44 |
|
simp2rr |
|
45 |
44
|
3expa |
|
46 |
41 43 45
|
3eqtrd |
|
47 |
26 27 1 2 16 28 39 46
|
kercvrlsm |
|
48 |
47
|
oveq2d |
|
49 |
16
|
ressid |
|
50 |
30 49
|
syl |
|
51 |
50
|
ad2antrr |
|
52 |
48 51
|
eqtr2d |
|
53 |
|
eqid |
|
54 |
|
eqid |
|
55 |
2 1 26
|
lmhmkerlss |
|
56 |
55
|
3ad2ant1 |
|
57 |
56
|
ad2antrr |
|
58 |
|
simpll2 |
|
59 |
|
inss2 |
|
60 |
59
|
sseli |
|
61 |
60
|
ad2antrl |
|
62 |
37 16 53
|
islssfgi |
|
63 |
31 36 61 62
|
syl3anc |
|
64 |
26 27 3 53 54 31 57 39 58 63
|
lsmfgcl |
|
65 |
52 64
|
eqeltrd |
|
66 |
25 65
|
rexlimddv |
|
67 |
14 66
|
rexlimddv |
|