Step |
Hyp |
Ref |
Expression |
1 |
|
usgr2pthlem.v |
|
2 |
|
usgr2pthlem.i |
|
3 |
|
0nn0 |
|
4 |
|
2nn0 |
|
5 |
|
0le2 |
|
6 |
|
elfz2nn0 |
|
7 |
3 4 5 6
|
mpbir3an |
|
8 |
|
ffvelrn |
|
9 |
7 8
|
mpan2 |
|
10 |
9
|
adantl |
|
11 |
|
1nn0 |
|
12 |
|
1le2 |
|
13 |
|
elfz2nn0 |
|
14 |
11 4 12 13
|
mpbir3an |
|
15 |
|
ffvelrn |
|
16 |
14 15
|
mpan2 |
|
17 |
16
|
adantl |
|
18 |
|
simpr |
|
19 |
|
fvex |
|
20 |
18 19
|
jctir |
|
21 |
|
prcom |
|
22 |
21
|
eqeq2i |
|
23 |
22
|
biimpi |
|
24 |
23
|
adantr |
|
25 |
24
|
ad2antlr |
|
26 |
2
|
usgrnloopv |
|
27 |
20 25 26
|
sylc |
|
28 |
27
|
adantr |
|
29 |
19
|
elsn |
|
30 |
29
|
necon3bbii |
|
31 |
28 30
|
sylibr |
|
32 |
17 31
|
eldifd |
|
33 |
32
|
adantr |
|
34 |
|
sneq |
|
35 |
34
|
difeq2d |
|
36 |
35
|
eleq2d |
|
37 |
36
|
adantl |
|
38 |
33 37
|
mpbird |
|
39 |
|
2re |
|
40 |
39
|
leidi |
|
41 |
|
elfz2nn0 |
|
42 |
4 4 40 41
|
mpbir3an |
|
43 |
|
ffvelrn |
|
44 |
42 43
|
mpan2 |
|
45 |
44
|
adantl |
|
46 |
2
|
usgrf1 |
|
47 |
46
|
ad2antlr |
|
48 |
|
simpl |
|
49 |
48
|
ad2antrr |
|
50 |
47 49
|
jca |
|
51 |
|
2nn |
|
52 |
|
lbfzo0 |
|
53 |
51 52
|
mpbir |
|
54 |
|
1lt2 |
|
55 |
|
elfzo0 |
|
56 |
11 51 54 55
|
mpbir3an |
|
57 |
53 56
|
pm3.2i |
|
58 |
57
|
a1i |
|
59 |
|
0ne1 |
|
60 |
59
|
a1i |
|
61 |
50 58 60
|
3jca |
|
62 |
|
simpr |
|
63 |
62
|
ad2antrr |
|
64 |
|
2f1fvneq |
|
65 |
61 63 64
|
sylc |
|
66 |
|
necom |
|
67 |
|
fvex |
|
68 |
|
fvex |
|
69 |
67 19 68
|
3pm3.2i |
|
70 |
|
fvexd |
|
71 |
|
simpl |
|
72 |
71
|
ad2antlr |
|
73 |
18 70 72
|
jca31 |
|
74 |
73
|
adantr |
|
75 |
2
|
usgrnloopv |
|
76 |
75
|
imp |
|
77 |
74 76
|
syl |
|
78 |
|
pr1nebg |
|
79 |
69 77 78
|
sylancr |
|
80 |
66 79
|
syl5bb |
|
81 |
65 80
|
mpbird |
|
82 |
|
fvexd |
|
83 |
|
prcom |
|
84 |
83
|
eqeq2i |
|
85 |
84
|
biimpi |
|
86 |
85
|
adantl |
|
87 |
86
|
ad2antlr |
|
88 |
18 82 87
|
jca31 |
|
89 |
88
|
adantr |
|
90 |
2
|
usgrnloopv |
|
91 |
90
|
imp |
|
92 |
89 91
|
syl |
|
93 |
81 92
|
nelprd |
|
94 |
45 93
|
eldifd |
|
95 |
94
|
ad2antrr |
|
96 |
|
preq12 |
|
97 |
96
|
difeq2d |
|
98 |
97
|
eleq2d |
|
99 |
98
|
adantll |
|
100 |
95 99
|
mpbird |
|
101 |
|
eqcom |
|
102 |
|
eqcom |
|
103 |
|
eqcom |
|
104 |
101 102 103
|
3anbi123i |
|
105 |
104
|
biimpi |
|
106 |
105
|
ad4ant123 |
|
107 |
101
|
biimpi |
|
108 |
107
|
ad2antrr |
|
109 |
102
|
biimpi |
|
110 |
109
|
ad2antlr |
|
111 |
108 110
|
preq12d |
|
112 |
111
|
eqeq2d |
|
113 |
103
|
biimpi |
|
114 |
113
|
adantl |
|
115 |
110 114
|
preq12d |
|
116 |
115
|
eqeq2d |
|
117 |
112 116
|
anbi12d |
|
118 |
117
|
biimpa |
|
119 |
106 118
|
jca |
|
120 |
119
|
exp41 |
|
121 |
120
|
adantl |
|
122 |
121
|
imp31 |
|
123 |
100 122
|
rspcimedv |
|
124 |
38 123
|
rspcimedv |
|
125 |
10 124
|
rspcimedv |
|
126 |
125
|
exp41 |
|
127 |
126
|
com15 |
|
128 |
127
|
pm2.43i |
|
129 |
128
|
com12 |
|
130 |
129
|
adantr |
|
131 |
|
oveq2 |
|
132 |
131
|
raleqdv |
|
133 |
|
fzo0to2pr |
|
134 |
133
|
raleqi |
|
135 |
|
2wlklem |
|
136 |
134 135
|
bitri |
|
137 |
132 136
|
bitrdi |
|
138 |
137
|
adantl |
|
139 |
|
oveq2 |
|
140 |
139
|
feq2d |
|
141 |
140
|
adantl |
|
142 |
|
f1eq2 |
|
143 |
131 142
|
syl |
|
144 |
143
|
imbi1d |
|
145 |
144
|
adantl |
|
146 |
141 145
|
imbi12d |
|
147 |
130 138 146
|
3imtr4d |
|
148 |
147
|
com14 |
|
149 |
148
|
com23 |
|
150 |
149
|
3imp |
|