Step |
Hyp |
Ref |
Expression |
1 |
|
itscnhlc0yqe.q |
|
2 |
|
itsclc0yqsol.d |
|
3 |
|
eqid |
|
4 |
|
eqid |
|
5 |
1 3 4
|
itsclc0yqe |
|
6 |
5
|
3adant1r |
|
7 |
6
|
3adant2r |
|
8 |
|
3simpa |
|
9 |
8
|
adantr |
|
10 |
1
|
resum2sqcl |
|
11 |
9 10
|
syl |
|
12 |
11
|
3ad2ant1 |
|
13 |
12
|
recnd |
|
14 |
|
simpr1 |
|
15 |
|
simpl |
|
16 |
|
simpr2 |
|
17 |
1
|
resum2sqgt0 |
|
18 |
14 15 16 17
|
syl21anc |
|
19 |
18
|
ex |
|
20 |
|
simpr2 |
|
21 |
|
simpl |
|
22 |
|
simpr1 |
|
23 |
|
eqid |
|
24 |
23
|
resum2sqgt0 |
|
25 |
20 21 22 24
|
syl21anc |
|
26 |
|
simp1 |
|
27 |
26
|
recnd |
|
28 |
27
|
sqcld |
|
29 |
|
simp2 |
|
30 |
29
|
recnd |
|
31 |
30
|
sqcld |
|
32 |
28 31
|
addcomd |
|
33 |
32
|
adantl |
|
34 |
1 33
|
syl5eq |
|
35 |
25 34
|
breqtrrd |
|
36 |
35
|
ex |
|
37 |
19 36
|
jaoi |
|
38 |
37
|
impcom |
|
39 |
38
|
gt0ne0d |
|
40 |
39
|
3ad2ant1 |
|
41 |
|
2cnd |
|
42 |
|
recn |
|
43 |
42
|
3ad2ant2 |
|
44 |
43
|
adantr |
|
45 |
44
|
3ad2ant1 |
|
46 |
|
recn |
|
47 |
46
|
3ad2ant3 |
|
48 |
47
|
adantr |
|
49 |
48
|
3ad2ant1 |
|
50 |
45 49
|
mulcld |
|
51 |
41 50
|
mulcld |
|
52 |
51
|
negcld |
|
53 |
49
|
sqcld |
|
54 |
|
recn |
|
55 |
54
|
3ad2ant1 |
|
56 |
55
|
adantr |
|
57 |
56
|
3ad2ant1 |
|
58 |
57
|
sqcld |
|
59 |
|
simpl |
|
60 |
59
|
rpcnd |
|
61 |
60
|
3ad2ant2 |
|
62 |
61
|
sqcld |
|
63 |
58 62
|
mulcld |
|
64 |
53 63
|
subcld |
|
65 |
|
recn |
|
66 |
65
|
adantl |
|
67 |
66
|
3ad2ant3 |
|
68 |
|
eqidd |
|
69 |
13 40 52 64 67 68
|
quad |
|
70 |
54
|
abscld |
|
71 |
70
|
recnd |
|
72 |
71
|
3ad2ant1 |
|
73 |
72
|
adantr |
|
74 |
73
|
3ad2ant1 |
|
75 |
59
|
rpred |
|
76 |
75
|
3ad2ant2 |
|
77 |
76
|
resqcld |
|
78 |
77 12
|
remulcld |
|
79 |
|
simp1l3 |
|
80 |
79
|
resqcld |
|
81 |
78 80
|
resubcld |
|
82 |
2 81
|
eqeltrid |
|
83 |
82
|
recnd |
|
84 |
83
|
sqrtcld |
|
85 |
41 74 84
|
mulassd |
|
86 |
85
|
oveq2d |
|
87 |
51
|
negnegd |
|
88 |
|
simpl |
|
89 |
88
|
3ad2ant1 |
|
90 |
|
simp2r |
|
91 |
1 3 4 2
|
itsclc0yqsollem2 |
|
92 |
89 76 90 91
|
syl3anc |
|
93 |
87 92
|
oveq12d |
|
94 |
74 84
|
mulcld |
|
95 |
41 50 94
|
adddid |
|
96 |
86 93 95
|
3eqtr4d |
|
97 |
96
|
oveq1d |
|
98 |
50 94
|
addcld |
|
99 |
|
2ne0 |
|
100 |
99
|
a1i |
|
101 |
98 13 41 40 100
|
divcan5d |
|
102 |
97 101
|
eqtrd |
|
103 |
102
|
eqeq2d |
|
104 |
85
|
oveq2d |
|
105 |
87 92
|
oveq12d |
|
106 |
41 50 94
|
subdid |
|
107 |
104 105 106
|
3eqtr4d |
|
108 |
107
|
oveq1d |
|
109 |
50 94
|
subcld |
|
110 |
109 13 41 40 100
|
divcan5d |
|
111 |
108 110
|
eqtrd |
|
112 |
111
|
eqeq2d |
|
113 |
103 112
|
orbi12d |
|
114 |
69 113
|
bitrd |
|
115 |
|
absid |
|
116 |
115
|
ex |
|
117 |
116
|
3ad2ant1 |
|
118 |
117
|
adantr |
|
119 |
118
|
3ad2ant1 |
|
120 |
119
|
impcom |
|
121 |
120
|
oveq1d |
|
122 |
121
|
oveq2d |
|
123 |
122
|
oveq1d |
|
124 |
123
|
eqeq2d |
|
125 |
121
|
oveq2d |
|
126 |
125
|
oveq1d |
|
127 |
126
|
eqeq2d |
|
128 |
124 127
|
orbi12d |
|
129 |
|
pm1.4 |
|
130 |
128 129
|
syl6bi |
|
131 |
50
|
adantl |
|
132 |
94
|
adantl |
|
133 |
131 132
|
subnegd |
|
134 |
74
|
adantl |
|
135 |
84
|
adantl |
|
136 |
134 135
|
mulneg1d |
|
137 |
89
|
simp1d |
|
138 |
137
|
adantl |
|
139 |
|
id |
|
140 |
|
0red |
|
141 |
139 140
|
ltnled |
|
142 |
|
ltle |
|
143 |
140 142
|
mpdan |
|
144 |
141 143
|
sylbird |
|
145 |
144
|
3ad2ant1 |
|
146 |
145
|
adantr |
|
147 |
146
|
3ad2ant1 |
|
148 |
147
|
impcom |
|
149 |
138 148
|
absnidd |
|
150 |
149
|
negeqd |
|
151 |
57
|
adantl |
|
152 |
151
|
negnegd |
|
153 |
150 152
|
eqtrd |
|
154 |
153
|
oveq1d |
|
155 |
136 154
|
eqtr3d |
|
156 |
155
|
oveq2d |
|
157 |
133 156
|
eqtr3d |
|
158 |
157
|
oveq1d |
|
159 |
158
|
eqeq2d |
|
160 |
131 132
|
negsubd |
|
161 |
155
|
oveq2d |
|
162 |
160 161
|
eqtr3d |
|
163 |
162
|
oveq1d |
|
164 |
163
|
eqeq2d |
|
165 |
159 164
|
orbi12d |
|
166 |
165
|
biimpd |
|
167 |
130 166
|
pm2.61ian |
|
168 |
114 167
|
sylbid |
|
169 |
7 168
|
syld |
|