Step |
Hyp |
Ref |
Expression |
1 |
|
ltrelnq |
|
2 |
1
|
brel |
|
3 |
2
|
simprd |
|
4 |
3
|
adantl |
|
5 |
|
breq2 |
|
6 |
5
|
anbi2d |
|
7 |
|
oveq2 |
|
8 |
7
|
eleq1d |
|
9 |
8
|
notbid |
|
10 |
9
|
rexbidv |
|
11 |
6 10
|
imbi12d |
|
12 |
|
prn0 |
|
13 |
|
n0 |
|
14 |
12 13
|
sylib |
|
15 |
14
|
adantr |
|
16 |
|
elprnq |
|
17 |
16
|
ad2ant2r |
|
18 |
|
mulidnq |
|
19 |
17 18
|
syl |
|
20 |
|
simplr |
|
21 |
|
ltmnq |
|
22 |
21
|
biimpa |
|
23 |
17 20 22
|
syl2anc |
|
24 |
19 23
|
eqbrtrrd |
|
25 |
1
|
brel |
|
26 |
25
|
simprd |
|
27 |
26
|
ad2antlr |
|
28 |
|
mulclnq |
|
29 |
17 27 28
|
syl2anc |
|
30 |
|
ltexnq |
|
31 |
29 30
|
syl |
|
32 |
24 31
|
mpbid |
|
33 |
|
simplll |
|
34 |
|
vex |
|
35 |
34
|
prlem934 |
|
36 |
33 35
|
syl |
|
37 |
33
|
adantr |
|
38 |
|
simprr |
|
39 |
|
eleq1 |
|
40 |
39
|
biimparc |
|
41 |
38 40
|
sylan |
|
42 |
41
|
adantr |
|
43 |
|
elprnq |
|
44 |
33 43
|
sylan |
|
45 |
|
elprnq |
|
46 |
|
addnqf |
|
47 |
46
|
fdmi |
|
48 |
|
0nnq |
|
49 |
47 48
|
ndmovrcl |
|
50 |
49
|
simprd |
|
51 |
45 50
|
syl |
|
52 |
33 41 51
|
syl2anc |
|
53 |
52
|
adantr |
|
54 |
|
addclnq |
|
55 |
44 53 54
|
syl2anc |
|
56 |
|
prub |
|
57 |
37 42 55 56
|
syl21anc |
|
58 |
27
|
ad2antrr |
|
59 |
|
mulclnq |
|
60 |
44 58 59
|
syl2anc |
|
61 |
17
|
ad2antrr |
|
62 |
|
simplr |
|
63 |
|
recclnq |
|
64 |
|
mulclnq |
|
65 |
63 64
|
sylan2 |
|
66 |
65
|
ancoms |
|
67 |
|
ltmnq |
|
68 |
66 67
|
syl |
|
69 |
|
mulassnq |
|
70 |
|
mulcomnq |
|
71 |
70
|
oveq2i |
|
72 |
69 71
|
eqtri |
|
73 |
|
recidnq |
|
74 |
73
|
oveq2d |
|
75 |
|
mulidnq |
|
76 |
74 75
|
sylan9eq |
|
77 |
72 76
|
syl5eq |
|
78 |
77
|
breq1d |
|
79 |
68 78
|
bitrd |
|
80 |
79
|
adantll |
|
81 |
|
mulnqf |
|
82 |
81
|
fdmi |
|
83 |
82 48
|
ndmovrcl |
|
84 |
83
|
simpld |
|
85 |
|
ltanq |
|
86 |
84 85
|
syl |
|
87 |
86
|
adantr |
|
88 |
|
vex |
|
89 |
|
ovex |
|
90 |
|
mulcomnq |
|
91 |
|
distrnq |
|
92 |
88 34 89 90 91
|
caovdir |
|
93 |
|
vex |
|
94 |
|
fvex |
|
95 |
|
mulassnq |
|
96 |
88 93 94 90 95
|
caov12 |
|
97 |
73
|
oveq2d |
|
98 |
|
mulidnq |
|
99 |
84 98
|
syl |
|
100 |
97 99
|
sylan9eqr |
|
101 |
96 100
|
syl5eq |
|
102 |
|
mulcomnq |
|
103 |
102
|
oveq2i |
|
104 |
|
mulassnq |
|
105 |
103 104
|
eqtr4i |
|
106 |
105
|
a1i |
|
107 |
101 106
|
oveq12d |
|
108 |
92 107
|
syl5eq |
|
109 |
108
|
breq2d |
|
110 |
87 109
|
bitr4d |
|
111 |
110
|
adantr |
|
112 |
80 111
|
bitrd |
|
113 |
112
|
adantrr |
|
114 |
|
ltanq |
|
115 |
|
addcomnq |
|
116 |
|
addcomnq |
|
117 |
115 116
|
breq12i |
|
118 |
114 117
|
bitrdi |
|
119 |
118
|
ad2antrl |
|
120 |
|
oveq1 |
|
121 |
|
vex |
|
122 |
88 121 93 90 95 94
|
caov411 |
|
123 |
73
|
oveq2d |
|
124 |
|
mulidnq |
|
125 |
123 124
|
sylan9eqr |
|
126 |
122 125
|
syl5eq |
|
127 |
120 126
|
sylan9eqr |
|
128 |
127
|
breq2d |
|
129 |
128
|
adantrl |
|
130 |
113 119 129
|
3bitr3d |
|
131 |
60 61 53 62 130
|
syl22anc |
|
132 |
57 131
|
sylibd |
|
133 |
|
prcdnq |
|
134 |
133
|
impancom |
|
135 |
134
|
con3d |
|
136 |
135
|
ex |
|
137 |
136
|
com23 |
|
138 |
37 137
|
syl |
|
139 |
132 138
|
mpdd |
|
140 |
139
|
reximdva |
|
141 |
36 140
|
mpd |
|
142 |
32 141
|
exlimddv |
|
143 |
142
|
expr |
|
144 |
|
oveq1 |
|
145 |
144
|
eleq1d |
|
146 |
145
|
notbid |
|
147 |
146
|
rspcev |
|
148 |
147
|
ex |
|
149 |
148
|
adantl |
|
150 |
143 149
|
pm2.61d |
|
151 |
15 150
|
exlimddv |
|
152 |
11 151
|
vtoclg |
|
153 |
4 152
|
mpcom |
|