Step |
Hyp |
Ref |
Expression |
1 |
|
3at.l |
|
2 |
|
3at.j |
|
3 |
|
3at.a |
|
4 |
|
oveq2 |
|
5 |
4
|
eqcoms |
|
6 |
5
|
breq2d |
|
7 |
5
|
eqeq2d |
|
8 |
6 7
|
imbi12d |
|
9 |
|
simp1l |
|
10 |
|
simp1r1 |
|
11 |
|
simp2 |
|
12 |
|
simp1r3 |
|
13 |
|
simp3 |
|
14 |
1 2 3
|
3atlem3 |
|
15 |
9 10 11 12 13 14
|
syl131anc |
|
16 |
15
|
3expia |
|
17 |
|
simp11 |
|
18 |
|
simp123 |
|
19 |
|
simp122 |
|
20 |
|
simp121 |
|
21 |
18 19 20
|
3jca |
|
22 |
|
simp131 |
|
23 |
|
simp132 |
|
24 |
22 23
|
jca |
|
25 |
|
simp21 |
|
26 |
|
simp22 |
|
27 |
1 2 3
|
hlatexch2 |
|
28 |
17 20 18 19 26 27
|
syl131anc |
|
29 |
25 28
|
mtod |
|
30 |
17
|
hllatd |
|
31 |
|
eqid |
|
32 |
31 3
|
atbase |
|
33 |
18 32
|
syl |
|
34 |
31 3
|
atbase |
|
35 |
20 34
|
syl |
|
36 |
31 3
|
atbase |
|
37 |
19 36
|
syl |
|
38 |
31 1 2
|
latnlej1r |
|
39 |
30 33 35 37 25 38
|
syl131anc |
|
40 |
|
simp3 |
|
41 |
1 2 3
|
3atlem4 |
|
42 |
17 21 24 29 39 40 41
|
syl321anc |
|
43 |
42
|
3expia |
|
44 |
|
simpl1 |
|
45 |
44
|
hllatd |
|
46 |
|
simpl21 |
|
47 |
46 34
|
syl |
|
48 |
|
simpl22 |
|
49 |
48 36
|
syl |
|
50 |
|
simpl23 |
|
51 |
50 32
|
syl |
|
52 |
31 2
|
latj31 |
|
53 |
45 47 49 51 52
|
syl13anc |
|
54 |
53
|
breq1d |
|
55 |
53
|
eqeq1d |
|
56 |
43 54 55
|
3imtr4d |
|
57 |
8 16 56
|
pm2.61ne |
|
58 |
57
|
3impia |
|