Step |
Hyp |
Ref |
Expression |
1 |
|
ballotth.m |
|
2 |
|
ballotth.n |
|
3 |
|
ballotth.o |
|
4 |
|
ballotth.p |
|
5 |
1 2 3
|
ballotlemoex |
|
6 |
|
ssrab2 |
|
7 |
5 6
|
elpwi2 |
|
8 |
|
fveq2 |
|
9 |
8
|
oveq1d |
|
10 |
|
ovex |
|
11 |
9 4 10
|
fvmpt |
|
12 |
7 11
|
ax-mp |
|
13 |
|
an32 |
|
14 |
|
2eluzge1 |
|
15 |
|
fzss1 |
|
16 |
14 15
|
ax-mp |
|
17 |
16
|
sspwi |
|
18 |
17
|
sseli |
|
19 |
|
1lt2 |
|
20 |
|
1re |
|
21 |
|
2re |
|
22 |
20 21
|
ltnlei |
|
23 |
19 22
|
mpbi |
|
24 |
|
elfzle1 |
|
25 |
23 24
|
mto |
|
26 |
|
elelpwi |
|
27 |
25 26
|
mto |
|
28 |
|
ancom |
|
29 |
27 28
|
mtbi |
|
30 |
29
|
imnani |
|
31 |
18 30
|
jca |
|
32 |
|
ssin |
|
33 |
|
1le2 |
|
34 |
|
1p1e2 |
|
35 |
|
nnge1 |
|
36 |
1 35
|
ax-mp |
|
37 |
|
nnge1 |
|
38 |
2 37
|
ax-mp |
|
39 |
1
|
nnrei |
|
40 |
2
|
nnrei |
|
41 |
20 20 39 40
|
le2addi |
|
42 |
36 38 41
|
mp2an |
|
43 |
34 42
|
eqbrtrri |
|
44 |
39 40
|
readdcli |
|
45 |
20 21 44
|
letri |
|
46 |
33 43 45
|
mp2an |
|
47 |
|
1z |
|
48 |
|
nnaddcl |
|
49 |
1 2 48
|
mp2an |
|
50 |
49
|
nnzi |
|
51 |
|
eluz |
|
52 |
47 50 51
|
mp2an |
|
53 |
46 52
|
mpbir |
|
54 |
|
elfzp12 |
|
55 |
53 54
|
ax-mp |
|
56 |
55
|
biimpi |
|
57 |
56
|
orcanai |
|
58 |
34
|
oveq1i |
|
59 |
57 58
|
eleqtrdi |
|
60 |
59
|
ss2abi |
|
61 |
|
inab |
|
62 |
|
abid2 |
|
63 |
62
|
ineq1i |
|
64 |
61 63
|
eqtr3i |
|
65 |
|
abid2 |
|
66 |
60 64 65
|
3sstr3i |
|
67 |
|
sstr |
|
68 |
66 67
|
mpan2 |
|
69 |
32 68
|
sylbi |
|
70 |
|
velpw |
|
71 |
|
ssab |
|
72 |
|
df-ex |
|
73 |
72
|
bicomi |
|
74 |
73
|
con1bii |
|
75 |
|
dfclel |
|
76 |
75
|
notbii |
|
77 |
|
imnang |
|
78 |
|
ancom |
|
79 |
78
|
notbii |
|
80 |
79
|
albii |
|
81 |
77 80
|
bitr4i |
|
82 |
74 76 81
|
3bitr4ri |
|
83 |
71 82
|
bitr2i |
|
84 |
70 83
|
anbi12i |
|
85 |
|
velpw |
|
86 |
69 84 85
|
3imtr4i |
|
87 |
31 86
|
impbii |
|
88 |
87
|
anbi1i |
|
89 |
3
|
rabeq2i |
|
90 |
89
|
anbi1i |
|
91 |
13 88 90
|
3bitr4i |
|
92 |
91
|
rabbia2 |
|
93 |
92
|
fveq2i |
|
94 |
|
fzfi |
|
95 |
1
|
nnzi |
|
96 |
|
hashbc |
|
97 |
94 95 96
|
mp2an |
|
98 |
|
2z |
|
99 |
98
|
eluz1i |
|
100 |
50 43 99
|
mpbir2an |
|
101 |
|
hashfz |
|
102 |
100 101
|
ax-mp |
|
103 |
1
|
nncni |
|
104 |
2
|
nncni |
|
105 |
103 104
|
addcli |
|
106 |
|
2cn |
|
107 |
|
ax-1cn |
|
108 |
|
subadd23 |
|
109 |
105 106 107 108
|
mp3an |
|
110 |
106 107
|
negsubdi2i |
|
111 |
|
2m1e1 |
|
112 |
111
|
negeqi |
|
113 |
110 112
|
eqtr3i |
|
114 |
113
|
oveq2i |
|
115 |
102 109 114
|
3eqtri |
|
116 |
105 107
|
negsubi |
|
117 |
115 116
|
eqtri |
|
118 |
117
|
oveq1i |
|
119 |
97 118
|
eqtr3i |
|
120 |
93 119
|
eqtr3i |
|
121 |
1 2 3
|
ballotlem1 |
|
122 |
120 121
|
oveq12i |
|
123 |
12 122
|
eqtri |
|
124 |
|
0le1 |
|
125 |
|
0re |
|
126 |
125 20 39
|
letri |
|
127 |
124 36 126
|
mp2an |
|
128 |
2
|
nngt0i |
|
129 |
40 128
|
elrpii |
|
130 |
|
ltaddrp |
|
131 |
39 129 130
|
mp2an |
|
132 |
|
0z |
|
133 |
|
elfzm11 |
|
134 |
132 50 133
|
mp2an |
|
135 |
95 127 131 134
|
mpbir3an |
|
136 |
|
bcm1n |
|
137 |
135 49 136
|
mp2an |
|
138 |
|
pncan2 |
|
139 |
103 104 138
|
mp2an |
|
140 |
139
|
oveq1i |
|
141 |
123 137 140
|
3eqtri |
|