Step |
Hyp |
Ref |
Expression |
1 |
|
sqff1o.1 |
|
2 |
|
sqff1o.2 |
|
3 |
|
sqff1o.3 |
|
4 |
|
fveq2 |
|
5 |
4
|
neeq1d |
|
6 |
|
breq1 |
|
7 |
5 6
|
anbi12d |
|
8 |
7 1
|
elrab2 |
|
9 |
8
|
simprbi |
|
10 |
9
|
simprd |
|
11 |
10
|
ad2antlr |
|
12 |
|
prmz |
|
13 |
12
|
adantl |
|
14 |
|
simplr |
|
15 |
14 8
|
sylib |
|
16 |
15
|
simpld |
|
17 |
16
|
nnzd |
|
18 |
|
nnz |
|
19 |
18
|
ad2antrr |
|
20 |
|
dvdstr |
|
21 |
13 17 19 20
|
syl3anc |
|
22 |
11 21
|
mpan2d |
|
23 |
22
|
ss2rabdv |
|
24 |
|
prmex |
|
25 |
24
|
rabex |
|
26 |
25
|
elpw |
|
27 |
23 26
|
sylibr |
|
28 |
|
cnveq |
|
29 |
28
|
imaeq1d |
|
30 |
29
|
eleq1d |
|
31 |
|
1nn0 |
|
32 |
|
0nn0 |
|
33 |
31 32
|
ifcli |
|
34 |
33
|
rgenw |
|
35 |
|
eqid |
|
36 |
35
|
fmpt |
|
37 |
34 36
|
mpbi |
|
38 |
37
|
a1i |
|
39 |
|
nn0ex |
|
40 |
39 24
|
elmap |
|
41 |
38 40
|
sylibr |
|
42 |
|
fzfi |
|
43 |
|
ffn |
|
44 |
|
elpreima |
|
45 |
37 43 44
|
mp2b |
|
46 |
|
elequ1 |
|
47 |
46
|
ifbid |
|
48 |
31 32
|
ifcli |
|
49 |
48
|
elexi |
|
50 |
47 35 49
|
fvmpt |
|
51 |
50
|
eleq1d |
|
52 |
51
|
biimpa |
|
53 |
45 52
|
sylbi |
|
54 |
|
0nnn |
|
55 |
|
iffalse |
|
56 |
55
|
eleq1d |
|
57 |
54 56
|
mtbiri |
|
58 |
57
|
con4i |
|
59 |
53 58
|
syl |
|
60 |
59
|
ssriv |
|
61 |
|
elpwi |
|
62 |
61
|
adantl |
|
63 |
|
prmssnn |
|
64 |
|
rabss2 |
|
65 |
63 64
|
ax-mp |
|
66 |
|
dvdsssfz1 |
|
67 |
66
|
adantr |
|
68 |
65 67
|
sstrid |
|
69 |
62 68
|
sstrd |
|
70 |
60 69
|
sstrid |
|
71 |
|
ssfi |
|
72 |
42 70 71
|
sylancr |
|
73 |
30 41 72
|
elrabd |
|
74 |
|
eqid |
|
75 |
3 74
|
1arith |
|
76 |
|
f1ocnv |
|
77 |
|
f1of |
|
78 |
75 76 77
|
mp2b |
|
79 |
78
|
ffvelrni |
|
80 |
73 79
|
syl |
|
81 |
|
f1ocnvfv2 |
|
82 |
75 73 81
|
sylancr |
|
83 |
3
|
1arithlem1 |
|
84 |
80 83
|
syl |
|
85 |
82 84
|
eqtr3d |
|
86 |
85
|
fveq1d |
|
87 |
|
elequ1 |
|
88 |
87
|
ifbid |
|
89 |
31 32
|
ifcli |
|
90 |
89
|
elexi |
|
91 |
88 35 90
|
fvmpt |
|
92 |
86 91
|
sylan9req |
|
93 |
|
oveq1 |
|
94 |
|
eqid |
|
95 |
|
ovex |
|
96 |
93 94 95
|
fvmpt |
|
97 |
96
|
adantl |
|
98 |
92 97
|
eqtr3d |
|
99 |
|
breq1 |
|
100 |
|
breq1 |
|
101 |
|
1le1 |
|
102 |
|
0le1 |
|
103 |
99 100 101 102
|
keephyp |
|
104 |
98 103
|
eqbrtrrdi |
|
105 |
104
|
ralrimiva |
|
106 |
|
issqf |
|
107 |
80 106
|
syl |
|
108 |
105 107
|
mpbird |
|
109 |
|
iftrue |
|
110 |
109
|
adantl |
|
111 |
62
|
sselda |
|
112 |
|
breq1 |
|
113 |
112
|
elrab |
|
114 |
111 113
|
sylib |
|
115 |
114
|
simprd |
|
116 |
114
|
simpld |
|
117 |
|
simpll |
|
118 |
|
pcelnn |
|
119 |
116 117 118
|
syl2anc |
|
120 |
115 119
|
mpbird |
|
121 |
120
|
nnge1d |
|
122 |
110 121
|
eqbrtrd |
|
123 |
122
|
ex |
|
124 |
123
|
adantr |
|
125 |
|
simpr |
|
126 |
18
|
ad2antrr |
|
127 |
|
pcge0 |
|
128 |
125 126 127
|
syl2anc |
|
129 |
|
iffalse |
|
130 |
129
|
breq1d |
|
131 |
128 130
|
syl5ibrcom |
|
132 |
124 131
|
pm2.61d |
|
133 |
98 132
|
eqbrtrrd |
|
134 |
133
|
ralrimiva |
|
135 |
80
|
nnzd |
|
136 |
18
|
adantr |
|
137 |
|
pc2dvds |
|
138 |
135 136 137
|
syl2anc |
|
139 |
134 138
|
mpbird |
|
140 |
108 139
|
jca |
|
141 |
|
fveq2 |
|
142 |
141
|
neeq1d |
|
143 |
|
breq1 |
|
144 |
142 143
|
anbi12d |
|
145 |
144 1
|
elrab2 |
|
146 |
80 140 145
|
sylanbrc |
|
147 |
|
eqcom |
|
148 |
8
|
simplbi |
|
149 |
148
|
ad2antrl |
|
150 |
24
|
mptex |
|
151 |
3
|
fvmpt2 |
|
152 |
149 150 151
|
sylancl |
|
153 |
152
|
eqeq1d |
|
154 |
75
|
a1i |
|
155 |
73
|
adantrl |
|
156 |
|
f1ocnvfvb |
|
157 |
154 149 155 156
|
syl3anc |
|
158 |
24
|
a1i |
|
159 |
|
0cnd |
|
160 |
|
1cnd |
|
161 |
|
0ne1 |
|
162 |
161
|
a1i |
|
163 |
158 159 160 162
|
pw2f1olem |
|
164 |
|
ssrab2 |
|
165 |
164
|
sspwi |
|
166 |
|
simprr |
|
167 |
165 166
|
sseldi |
|
168 |
167
|
biantrurd |
|
169 |
|
id |
|
170 |
148
|
adantl |
|
171 |
|
pccl |
|
172 |
169 170 171
|
syl2anr |
|
173 |
|
elnn0 |
|
174 |
172 173
|
sylib |
|
175 |
174
|
orcomd |
|
176 |
9
|
simpld |
|
177 |
176
|
adantl |
|
178 |
|
issqf |
|
179 |
170 178
|
syl |
|
180 |
177 179
|
mpbid |
|
181 |
180
|
r19.21bi |
|
182 |
|
nnle1eq1 |
|
183 |
181 182
|
syl5ibcom |
|
184 |
183
|
orim2d |
|
185 |
175 184
|
mpd |
|
186 |
|
ovex |
|
187 |
186
|
elpr |
|
188 |
185 187
|
sylibr |
|
189 |
188
|
fmpttd |
|
190 |
189
|
adantrr |
|
191 |
|
prex |
|
192 |
191 24
|
elmap |
|
193 |
190 192
|
sylibr |
|
194 |
193
|
biantrurd |
|
195 |
163 168 194
|
3bitr4d |
|
196 |
|
eqid |
|
197 |
196
|
mptiniseg |
|
198 |
31 197
|
ax-mp |
|
199 |
|
id |
|
200 |
|
1nn |
|
201 |
199 200
|
eqeltrdi |
|
202 |
201 183
|
impbid2 |
|
203 |
|
simpr |
|
204 |
|
pcelnn |
|
205 |
203 16 204
|
syl2anc |
|
206 |
202 205
|
bitrd |
|
207 |
206
|
rabbidva |
|
208 |
207
|
adantrr |
|
209 |
198 208
|
syl5eq |
|
210 |
209
|
eqeq2d |
|
211 |
195 210
|
bitrd |
|
212 |
153 157 211
|
3bitr3d |
|
213 |
147 212
|
syl5bb |
|
214 |
2 27 146 213
|
f1o2d |
|