Step |
Hyp |
Ref |
Expression |
1 |
|
lsmssass.p |
|
2 |
|
lsmssass.b |
|
3 |
|
lsmssass.g |
|
4 |
|
lsmssass.r |
|
5 |
|
lsmssass.t |
|
6 |
|
lsmssass.u |
|
7 |
|
eqid |
|
8 |
2 7 1
|
lsmvalx |
|
9 |
3 4 5 8
|
syl3anc |
|
10 |
9
|
rexeqdv |
|
11 |
|
ovex |
|
12 |
11
|
rgen2w |
|
13 |
|
eqid |
|
14 |
|
oveq1 |
|
15 |
14
|
eqeq2d |
|
16 |
15
|
rexbidv |
|
17 |
13 16
|
rexrnmpo |
|
18 |
12 17
|
ax-mp |
|
19 |
10 18
|
bitrdi |
|
20 |
2 7 1
|
lsmvalx |
|
21 |
3 5 6 20
|
syl3anc |
|
22 |
21
|
rexeqdv |
|
23 |
|
ovex |
|
24 |
23
|
rgen2w |
|
25 |
|
eqid |
|
26 |
|
oveq2 |
|
27 |
26
|
eqeq2d |
|
28 |
25 27
|
rexrnmpo |
|
29 |
24 28
|
ax-mp |
|
30 |
22 29
|
bitrdi |
|
31 |
30
|
adantr |
|
32 |
3
|
ad2antrr |
|
33 |
4
|
ad2antrr |
|
34 |
|
simplr |
|
35 |
33 34
|
sseldd |
|
36 |
5
|
ad2antrr |
|
37 |
|
simprl |
|
38 |
36 37
|
sseldd |
|
39 |
6
|
ad2antrr |
|
40 |
|
simprr |
|
41 |
39 40
|
sseldd |
|
42 |
2 7
|
mndass |
|
43 |
32 35 38 41 42
|
syl13anc |
|
44 |
43
|
eqeq2d |
|
45 |
44
|
2rexbidva |
|
46 |
31 45
|
bitr4d |
|
47 |
46
|
rexbidva |
|
48 |
19 47
|
bitr4d |
|
49 |
2 1
|
lsmssv |
|
50 |
3 4 5 49
|
syl3anc |
|
51 |
2 7 1
|
lsmelvalx |
|
52 |
3 50 6 51
|
syl3anc |
|
53 |
2 1
|
lsmssv |
|
54 |
3 5 6 53
|
syl3anc |
|
55 |
2 7 1
|
lsmelvalx |
|
56 |
3 4 54 55
|
syl3anc |
|
57 |
48 52 56
|
3bitr4d |
|
58 |
57
|
eqrdv |
|