Step |
Hyp |
Ref |
Expression |
1 |
|
ltrelnq |
|
2 |
1
|
brel |
|
3 |
|
ordpinq |
|
4 |
|
elpqn |
|
5 |
4
|
adantr |
|
6 |
|
xp1st |
|
7 |
5 6
|
syl |
|
8 |
|
elpqn |
|
9 |
8
|
adantl |
|
10 |
|
xp2nd |
|
11 |
9 10
|
syl |
|
12 |
|
mulclpi |
|
13 |
7 11 12
|
syl2anc |
|
14 |
|
xp1st |
|
15 |
9 14
|
syl |
|
16 |
|
xp2nd |
|
17 |
5 16
|
syl |
|
18 |
|
mulclpi |
|
19 |
15 17 18
|
syl2anc |
|
20 |
|
ltexpi |
|
21 |
13 19 20
|
syl2anc |
|
22 |
|
relxp |
|
23 |
4
|
ad2antrr |
|
24 |
|
1st2nd |
|
25 |
22 23 24
|
sylancr |
|
26 |
25
|
oveq1d |
|
27 |
7
|
adantr |
|
28 |
17
|
adantr |
|
29 |
|
simpr |
|
30 |
|
mulclpi |
|
31 |
17 11 30
|
syl2anc |
|
32 |
31
|
adantr |
|
33 |
|
addpipq |
|
34 |
27 28 29 32 33
|
syl22anc |
|
35 |
26 34
|
eqtrd |
|
36 |
|
oveq2 |
|
37 |
|
distrpi |
|
38 |
|
fvex |
|
39 |
|
fvex |
|
40 |
|
fvex |
|
41 |
|
mulcompi |
|
42 |
|
mulasspi |
|
43 |
38 39 40 41 42
|
caov12 |
|
44 |
|
mulcompi |
|
45 |
43 44
|
oveq12i |
|
46 |
37 45
|
eqtr2i |
|
47 |
|
mulasspi |
|
48 |
|
mulcompi |
|
49 |
48
|
oveq2i |
|
50 |
47 49
|
eqtri |
|
51 |
36 46 50
|
3eqtr4g |
|
52 |
|
mulasspi |
|
53 |
52
|
eqcomi |
|
54 |
53
|
a1i |
|
55 |
51 54
|
opeq12d |
|
56 |
55
|
eqeq2d |
|
57 |
35 56
|
syl5ibcom |
|
58 |
|
fveq2 |
|
59 |
|
adderpq |
|
60 |
|
nqerid |
|
61 |
60
|
ad2antrr |
|
62 |
61
|
oveq1d |
|
63 |
59 62
|
syl5eqr |
|
64 |
|
mulclpi |
|
65 |
17 17 64
|
syl2anc |
|
66 |
65
|
adantr |
|
67 |
15
|
adantr |
|
68 |
11
|
adantr |
|
69 |
|
mulcanenq |
|
70 |
66 67 68 69
|
syl3anc |
|
71 |
8
|
ad2antlr |
|
72 |
|
1st2nd |
|
73 |
22 71 72
|
sylancr |
|
74 |
70 73
|
breqtrrd |
|
75 |
|
mulclpi |
|
76 |
66 67 75
|
syl2anc |
|
77 |
|
mulclpi |
|
78 |
66 68 77
|
syl2anc |
|
79 |
76 78
|
opelxpd |
|
80 |
|
nqereq |
|
81 |
79 71 80
|
syl2anc |
|
82 |
74 81
|
mpbid |
|
83 |
|
nqerid |
|
84 |
83
|
ad2antlr |
|
85 |
82 84
|
eqtrd |
|
86 |
63 85
|
eqeq12d |
|
87 |
58 86
|
syl5ib |
|
88 |
57 87
|
syld |
|
89 |
|
fvex |
|
90 |
|
oveq2 |
|
91 |
90
|
eqeq1d |
|
92 |
89 91
|
spcev |
|
93 |
88 92
|
syl6 |
|
94 |
93
|
rexlimdva |
|
95 |
21 94
|
sylbid |
|
96 |
3 95
|
sylbid |
|
97 |
2 96
|
mpcom |
|
98 |
|
eleq1 |
|
99 |
98
|
biimparc |
|
100 |
|
addnqf |
|
101 |
100
|
fdmi |
|
102 |
|
0nnq |
|
103 |
101 102
|
ndmovrcl |
|
104 |
|
ltaddnq |
|
105 |
99 103 104
|
3syl |
|
106 |
|
simpr |
|
107 |
105 106
|
breqtrd |
|
108 |
107
|
ex |
|
109 |
108
|
exlimdv |
|
110 |
97 109
|
impbid2 |
|