Step |
Hyp |
Ref |
Expression |
1 |
|
1xr |
|
2 |
|
0le1 |
|
3 |
|
pnfge |
|
4 |
1 3
|
ax-mp |
|
5 |
|
0xr |
|
6 |
|
pnfxr |
|
7 |
|
elicc1 |
|
8 |
5 6 7
|
mp2an |
|
9 |
1 2 4 8
|
mpbir3an |
|
10 |
|
0e0iccpnf |
|
11 |
9 10
|
ifcli |
|
12 |
11
|
rgenw |
|
13 |
|
df-dde |
|
14 |
13
|
fmpt |
|
15 |
12 14
|
mpbi |
|
16 |
|
0ss |
|
17 |
|
noel |
|
18 |
|
ddeval0 |
|
19 |
16 17 18
|
mp2an |
|
20 |
|
rabxm |
|
21 |
|
esumeq1 |
|
22 |
20 21
|
ax-mp |
|
23 |
|
nfv |
|
24 |
|
nfcv |
|
25 |
|
nfcv |
|
26 |
|
rabexg |
|
27 |
|
rabexg |
|
28 |
|
rabnc |
|
29 |
28
|
a1i |
|
30 |
|
elrabi |
|
31 |
30
|
adantl |
|
32 |
|
simpl |
|
33 |
|
elelpwi |
|
34 |
31 32 33
|
syl2anc |
|
35 |
15
|
ffvelrni |
|
36 |
34 35
|
syl |
|
37 |
|
elrabi |
|
38 |
37
|
adantl |
|
39 |
|
simpl |
|
40 |
38 39 33
|
syl2anc |
|
41 |
40 35
|
syl |
|
42 |
23 24 25 26 27 29 36 41
|
esumsplit |
|
43 |
22 42
|
syl5eq |
|
44 |
43
|
adantr |
|
45 |
|
esumeq1 |
|
46 |
45
|
adantl |
|
47 |
|
simp-4l |
|
48 |
|
vex |
|
49 |
48
|
rabsnel |
|
50 |
49
|
adantl |
|
51 |
|
eleq2w |
|
52 |
48 51
|
rabsnt |
|
53 |
52
|
adantl |
|
54 |
|
elelpwi |
|
55 |
54
|
ancoms |
|
56 |
55
|
adantrr |
|
57 |
|
simpr |
|
58 |
57
|
fveq2d |
|
59 |
48
|
a1i |
|
60 |
15
|
ffvelrni |
|
61 |
58 59 60
|
esumsn |
|
62 |
56 61
|
syl |
|
63 |
56
|
elpwid |
|
64 |
|
simprr |
|
65 |
|
ddeval1 |
|
66 |
63 64 65
|
syl2anc |
|
67 |
62 66
|
eqtrd |
|
68 |
47 50 53 67
|
syl12anc |
|
69 |
46 68
|
eqtrd |
|
70 |
|
df-disj |
|
71 |
|
c0ex |
|
72 |
|
eleq1 |
|
73 |
72
|
rmobidv |
|
74 |
71 73
|
spcv |
|
75 |
70 74
|
sylbi |
|
76 |
|
rmo5 |
|
77 |
76
|
biimpi |
|
78 |
77
|
imp |
|
79 |
75 78
|
sylan |
|
80 |
|
reusn |
|
81 |
79 80
|
sylib |
|
82 |
|
eleq2w |
|
83 |
82
|
cbvrabv |
|
84 |
83
|
eqeq1i |
|
85 |
49
|
ancri |
|
86 |
84 85
|
sylbir |
|
87 |
86
|
eximi |
|
88 |
|
df-rex |
|
89 |
87 88
|
sylibr |
|
90 |
81 89
|
syl |
|
91 |
90
|
adantll |
|
92 |
69 91
|
r19.29a |
|
93 |
|
elpwi |
|
94 |
|
sspwuni |
|
95 |
93 94
|
sylib |
|
96 |
|
eluni2 |
|
97 |
96
|
biimpri |
|
98 |
|
ddeval1 |
|
99 |
95 97 98
|
syl2an |
|
100 |
99
|
adantlr |
|
101 |
92 100
|
eqtr4d |
|
102 |
|
nfre1 |
|
103 |
102
|
nfn |
|
104 |
82
|
elrab |
|
105 |
104
|
exbii |
|
106 |
|
neq0 |
|
107 |
|
df-rex |
|
108 |
105 106 107
|
3bitr4i |
|
109 |
108
|
biimpi |
|
110 |
109
|
con1i |
|
111 |
103 110
|
esumeq1d |
|
112 |
|
esumnul |
|
113 |
111 112
|
eqtrdi |
|
114 |
113
|
adantl |
|
115 |
96
|
biimpi |
|
116 |
115
|
con3i |
|
117 |
|
ddeval0 |
|
118 |
95 116 117
|
syl2an |
|
119 |
118
|
adantlr |
|
120 |
114 119
|
eqtr4d |
|
121 |
101 120
|
pm2.61dan |
|
122 |
40
|
elpwid |
|
123 |
82
|
notbid |
|
124 |
123
|
elrab |
|
125 |
124
|
simprbi |
|
126 |
125
|
adantl |
|
127 |
|
ddeval0 |
|
128 |
122 126 127
|
syl2anc |
|
129 |
128
|
esumeq2dv |
|
130 |
|
vex |
|
131 |
130
|
rabex |
|
132 |
25
|
esum0 |
|
133 |
131 132
|
ax-mp |
|
134 |
129 133
|
eqtrdi |
|
135 |
134
|
adantr |
|
136 |
121 135
|
oveq12d |
|
137 |
|
vuniex |
|
138 |
137
|
elpw |
|
139 |
138
|
biimpri |
|
140 |
|
iccssxr |
|
141 |
15
|
ffvelrni |
|
142 |
140 141
|
sselid |
|
143 |
|
xaddid1 |
|
144 |
95 139 142 143
|
4syl |
|
145 |
144
|
adantr |
|
146 |
44 136 145
|
3eqtrrd |
|
147 |
146
|
adantrl |
|
148 |
147
|
ex |
|
149 |
148
|
rgen |
|
150 |
|
reex |
|
151 |
|
pwsiga |
|
152 |
150 151
|
ax-mp |
|
153 |
|
elrnsiga |
|
154 |
|
ismeas |
|
155 |
152 153 154
|
mp2b |
|
156 |
15 19 149 155
|
mpbir3an |
|