Step |
Hyp |
Ref |
Expression |
1 |
|
line2ylem.i |
|
2 |
|
line2ylem.p |
|
3 |
|
ianor |
|
4 |
|
df-ne |
|
5 |
|
0re |
|
6 |
1 2
|
prelrrx2 |
|
7 |
5 5 6
|
mp2an |
|
8 |
|
eqneqall |
|
9 |
8
|
com12 |
|
10 |
|
eqid |
|
11 |
10
|
pm2.24i |
|
12 |
9 11
|
impbid1 |
|
13 |
12
|
adantl |
|
14 |
|
xor3 |
|
15 |
13 14
|
sylibr |
|
16 |
|
simp1 |
|
17 |
16
|
recnd |
|
18 |
17
|
mul01d |
|
19 |
|
simp2 |
|
20 |
19
|
recnd |
|
21 |
20
|
mul01d |
|
22 |
18 21
|
oveq12d |
|
23 |
|
00id |
|
24 |
22 23
|
eqtrdi |
|
25 |
24
|
eqeq1d |
|
26 |
|
eqcom |
|
27 |
25 26
|
syl6bb |
|
28 |
27
|
adantr |
|
29 |
28
|
bibi1d |
|
30 |
15 29
|
mtbird |
|
31 |
|
fveq1 |
|
32 |
|
1ex |
|
33 |
|
c0ex |
|
34 |
|
1ne2 |
|
35 |
|
fvpr1g |
|
36 |
32 33 34 35
|
mp3an |
|
37 |
31 36
|
eqtrdi |
|
38 |
37
|
oveq2d |
|
39 |
|
fveq1 |
|
40 |
|
2ex |
|
41 |
|
fvpr2g |
|
42 |
40 33 34 41
|
mp3an |
|
43 |
39 42
|
eqtrdi |
|
44 |
43
|
oveq2d |
|
45 |
38 44
|
oveq12d |
|
46 |
45
|
eqeq1d |
|
47 |
37
|
eqeq1d |
|
48 |
46 47
|
bibi12d |
|
49 |
48
|
notbid |
|
50 |
49
|
rspcev |
|
51 |
7 30 50
|
sylancr |
|
52 |
51
|
expcom |
|
53 |
4 52
|
sylbir |
|
54 |
|
notnotb |
|
55 |
|
ianor |
|
56 |
|
df-ne |
|
57 |
|
1red |
|
58 |
16
|
adantr |
|
59 |
58
|
renegcld |
|
60 |
19
|
adantr |
|
61 |
|
simprl |
|
62 |
59 60 61
|
redivcld |
|
63 |
1 2
|
prelrrx2 |
|
64 |
57 62 63
|
syl2anc |
|
65 |
|
ax-1ne0 |
|
66 |
65
|
neii |
|
67 |
10 66
|
2th |
|
68 |
|
xor3 |
|
69 |
67 68
|
mpbir |
|
70 |
17
|
mulid1d |
|
71 |
70
|
adantr |
|
72 |
17
|
negcld |
|
73 |
72
|
adantr |
|
74 |
20
|
adantr |
|
75 |
73 74 61
|
divcan2d |
|
76 |
71 75
|
oveq12d |
|
77 |
17
|
negidd |
|
78 |
77
|
adantr |
|
79 |
76 78
|
eqtrd |
|
80 |
|
simprr |
|
81 |
79 80
|
eqeq12d |
|
82 |
81
|
bibi1d |
|
83 |
69 82
|
mtbiri |
|
84 |
|
fveq1 |
|
85 |
|
fvpr1g |
|
86 |
32 32 34 85
|
mp3an |
|
87 |
84 86
|
eqtrdi |
|
88 |
87
|
oveq2d |
|
89 |
|
fveq1 |
|
90 |
|
ovex |
|
91 |
|
fvpr2g |
|
92 |
40 90 34 91
|
mp3an |
|
93 |
89 92
|
eqtrdi |
|
94 |
93
|
oveq2d |
|
95 |
88 94
|
oveq12d |
|
96 |
95
|
eqeq1d |
|
97 |
87
|
eqeq1d |
|
98 |
96 97
|
bibi12d |
|
99 |
98
|
notbid |
|
100 |
99
|
rspcev |
|
101 |
64 83 100
|
syl2anc |
|
102 |
101
|
expcom |
|
103 |
102
|
ex |
|
104 |
56 103
|
sylbir |
|
105 |
|
notnotb |
|
106 |
|
nne |
|
107 |
106
|
bicomi |
|
108 |
|
1re |
|
109 |
1 2
|
prelrrx2 |
|
110 |
108 108 109
|
mp2an |
|
111 |
|
oveq1 |
|
112 |
111
|
adantl |
|
113 |
|
ax-1cn |
|
114 |
113
|
mul02i |
|
115 |
112 114
|
eqtrdi |
|
116 |
|
oveq1 |
|
117 |
116
|
adantr |
|
118 |
117 114
|
eqtrdi |
|
119 |
115 118
|
oveq12d |
|
120 |
119 23
|
eqtrdi |
|
121 |
|
id |
|
122 |
120 121
|
eqeqan12d |
|
123 |
122
|
bibi1d |
|
124 |
69 123
|
mtbiri |
|
125 |
|
fveq1 |
|
126 |
|
fvpr1g |
|
127 |
32 32 34 126
|
mp3an |
|
128 |
125 127
|
eqtrdi |
|
129 |
128
|
oveq2d |
|
130 |
|
fveq1 |
|
131 |
|
fvpr2g |
|
132 |
40 32 34 131
|
mp3an |
|
133 |
130 132
|
eqtrdi |
|
134 |
133
|
oveq2d |
|
135 |
129 134
|
oveq12d |
|
136 |
135
|
eqeq1d |
|
137 |
128
|
eqeq1d |
|
138 |
136 137
|
bibi12d |
|
139 |
138
|
notbid |
|
140 |
139
|
rspcev |
|
141 |
110 124 140
|
sylancr |
|
142 |
141
|
a1d |
|
143 |
142
|
ex |
|
144 |
105 107 143
|
syl2anbr |
|
145 |
104 144
|
jaoi3 |
|
146 |
145
|
orcoms |
|
147 |
55 146
|
sylbi |
|
148 |
147
|
com12 |
|
149 |
54 148
|
sylbir |
|
150 |
149
|
imp |
|
151 |
53 150
|
jaoi3 |
|
152 |
151
|
orcoms |
|
153 |
152
|
com12 |
|
154 |
3 153
|
syl5bi |
|
155 |
|
rexnal |
|
156 |
154 155
|
syl6ib |
|
157 |
156
|
con4d |
|
158 |
|
df-3an |
|
159 |
157 158
|
syl6ibr |
|