Step |
Hyp |
Ref |
Expression |
1 |
|
nfdisj1 |
|
2 |
|
nfv |
|
3 |
|
nfv |
|
4 |
1 2 3
|
nf3an |
|
5 |
|
simp2 |
|
6 |
|
simp3 |
|
7 |
|
simp1 |
|
8 |
4 5 6 7
|
hashunif |
|
9 |
|
simpl |
|
10 |
|
dfss3 |
|
11 |
|
hashcl |
|
12 |
|
nn0re |
|
13 |
|
nn0ge0 |
|
14 |
|
elrege0 |
|
15 |
12 13 14
|
sylanbrc |
|
16 |
11 15
|
syl |
|
17 |
16
|
ralimi |
|
18 |
10 17
|
sylbi |
|
19 |
18
|
r19.21bi |
|
20 |
19
|
adantll |
|
21 |
9 20
|
esumpfinval |
|
22 |
21
|
3adant1 |
|
23 |
8 22
|
eqtr4d |
|
24 |
23
|
3adant1l |
|
25 |
24
|
3expa |
|
26 |
|
uniexg |
|
27 |
10
|
notbii |
|
28 |
|
rexnal |
|
29 |
27 28
|
bitr4i |
|
30 |
|
elssuni |
|
31 |
|
ssfi |
|
32 |
31
|
expcom |
|
33 |
32
|
con3d |
|
34 |
30 33
|
syl |
|
35 |
34
|
rexlimiv |
|
36 |
29 35
|
sylbi |
|
37 |
|
hashinf |
|
38 |
26 36 37
|
syl2an |
|
39 |
|
vex |
|
40 |
|
hashinf |
|
41 |
39 40
|
mpan |
|
42 |
41
|
reximi |
|
43 |
29 42
|
sylbi |
|
44 |
|
nfv |
|
45 |
|
nfre1 |
|
46 |
44 45
|
nfan |
|
47 |
|
simpl |
|
48 |
|
hashf2 |
|
49 |
|
ffvelrn |
|
50 |
48 39 49
|
mp2an |
|
51 |
50
|
a1i |
|
52 |
|
simpr |
|
53 |
46 47 51 52
|
esumpinfval |
|
54 |
43 53
|
sylan2 |
|
55 |
38 54
|
eqtr4d |
|
56 |
55
|
3adant2 |
|
57 |
56
|
3adant1r |
|
58 |
57
|
3expa |
|
59 |
25 58
|
pm2.61dan |
|
60 |
|
pwfi |
|
61 |
|
pwuni |
|
62 |
|
ssfi |
|
63 |
61 62
|
mpan2 |
|
64 |
60 63
|
sylbi |
|
65 |
64
|
con3i |
|
66 |
26 65 37
|
syl2an |
|
67 |
|
nftru |
|
68 |
|
unrab |
|
69 |
|
exmid |
|
70 |
69
|
rgenw |
|
71 |
|
rabid2 |
|
72 |
70 71
|
mpbir |
|
73 |
68 72
|
eqtr4i |
|
74 |
73
|
a1i |
|
75 |
67 74
|
esumeq1d |
|
76 |
75
|
mptru |
|
77 |
|
nfrab1 |
|
78 |
|
nfrab1 |
|
79 |
|
rabexg |
|
80 |
|
rabexg |
|
81 |
|
rabnc |
|
82 |
81
|
a1i |
|
83 |
50
|
a1i |
|
84 |
50
|
a1i |
|
85 |
44 77 78 79 80 82 83 84
|
esumsplit |
|
86 |
76 85
|
syl5eqr |
|
87 |
86
|
adantr |
|
88 |
|
nfv |
|
89 |
80
|
adantr |
|
90 |
|
simpr |
|
91 |
|
dfrab3 |
|
92 |
|
hasheq0 |
|
93 |
39 92
|
ax-mp |
|
94 |
93
|
abbii |
|
95 |
|
df-sn |
|
96 |
94 95
|
eqtr4i |
|
97 |
96
|
ineq2i |
|
98 |
91 97
|
eqtri |
|
99 |
|
snfi |
|
100 |
|
inss2 |
|
101 |
|
ssfi |
|
102 |
99 100 101
|
mp2an |
|
103 |
98 102
|
eqeltri |
|
104 |
103
|
a1i |
|
105 |
|
difinf |
|
106 |
90 104 105
|
syl2anc |
|
107 |
|
notrab |
|
108 |
107
|
eleq1i |
|
109 |
106 108
|
sylnib |
|
110 |
50
|
a1i |
|
111 |
39
|
a1i |
|
112 |
|
simpr |
|
113 |
|
rabid |
|
114 |
112 113
|
sylib |
|
115 |
114
|
simprd |
|
116 |
93
|
biimpri |
|
117 |
116
|
necon3bi |
|
118 |
115 117
|
syl |
|
119 |
|
hashge1 |
|
120 |
111 118 119
|
syl2anc |
|
121 |
|
1xr |
|
122 |
121
|
a1i |
|
123 |
|
0lt1 |
|
124 |
123
|
a1i |
|
125 |
88 78 89 109 110 120 122 124
|
esumpinfsum |
|
126 |
125
|
oveq2d |
|
127 |
|
iccssxr |
|
128 |
79
|
adantr |
|
129 |
50
|
a1i |
|
130 |
129
|
ralrimiva |
|
131 |
77
|
esumcl |
|
132 |
128 130 131
|
syl2anc |
|
133 |
127 132
|
sseldi |
|
134 |
|
xrge0neqmnf |
|
135 |
132 134
|
syl |
|
136 |
|
xaddpnf1 |
|
137 |
133 135 136
|
syl2anc |
|
138 |
87 126 137
|
3eqtrd |
|
139 |
66 138
|
eqtr4d |
|
140 |
139
|
adantlr |
|
141 |
59 140
|
pm2.61dan |
|