Step |
Hyp |
Ref |
Expression |
1 |
|
refsum2cnlem1.1 |
|
2 |
|
refsum2cnlem1.2 |
|
3 |
|
refsum2cnlem1.3 |
|
4 |
|
refsum2cnlem1.4 |
|
5 |
|
refsum2cnlem1.5 |
|
6 |
|
refsum2cnlem1.6 |
|
7 |
|
refsum2cnlem1.7 |
|
8 |
|
refsum2cnlem1.8 |
|
9 |
|
refsum2cnlem1.9 |
|
10 |
|
nfmpt1 |
|
11 |
5 10
|
nfcxfr |
|
12 |
|
nfcv |
|
13 |
11 12
|
nffv |
|
14 |
|
nfcv |
|
15 |
13 14
|
nffv |
|
16 |
15
|
a1i |
|
17 |
|
nfcv |
|
18 |
11 17
|
nffv |
|
19 |
18 14
|
nffv |
|
20 |
19
|
a1i |
|
21 |
|
1cnd |
|
22 |
|
2cnd |
|
23 |
|
1ex |
|
24 |
23
|
prid1 |
|
25 |
8 9
|
ifcld |
|
26 |
|
eqeq1 |
|
27 |
26
|
ifbid |
|
28 |
27 5
|
fvmptg |
|
29 |
24 25 28
|
sylancr |
|
30 |
|
eqid |
|
31 |
30
|
iftruei |
|
32 |
29 31
|
eqtrdi |
|
33 |
32
|
adantr |
|
34 |
33
|
fveq1d |
|
35 |
|
eqid |
|
36 |
|
eqid |
|
37 |
35 36
|
cnf |
|
38 |
8 37
|
syl |
|
39 |
|
toponuni |
|
40 |
7 39
|
syl |
|
41 |
40
|
eqcomd |
|
42 |
6
|
unieqi |
|
43 |
|
uniretop |
|
44 |
42 43
|
eqtr4i |
|
45 |
44
|
a1i |
|
46 |
41 45
|
feq23d |
|
47 |
38 46
|
mpbid |
|
48 |
47
|
anim1i |
|
49 |
|
ffvelrn |
|
50 |
|
recn |
|
51 |
48 49 50
|
3syl |
|
52 |
34 51
|
eqeltrd |
|
53 |
|
2ex |
|
54 |
53
|
prid2 |
|
55 |
8 9
|
ifcld |
|
56 |
|
eqeq1 |
|
57 |
56
|
ifbid |
|
58 |
57 5
|
fvmptg |
|
59 |
54 55 58
|
sylancr |
|
60 |
|
1ne2 |
|
61 |
60
|
nesymi |
|
62 |
61
|
iffalsei |
|
63 |
59 62
|
eqtrdi |
|
64 |
63
|
adantr |
|
65 |
64
|
fveq1d |
|
66 |
35 36
|
cnf |
|
67 |
9 66
|
syl |
|
68 |
41 45
|
feq23d |
|
69 |
67 68
|
mpbid |
|
70 |
69
|
anim1i |
|
71 |
|
ffvelrn |
|
72 |
|
recn |
|
73 |
70 71 72
|
3syl |
|
74 |
65 73
|
eqeltrd |
|
75 |
60
|
a1i |
|
76 |
|
fveq2 |
|
77 |
76
|
fveq1d |
|
78 |
77
|
adantl |
|
79 |
|
fveq2 |
|
80 |
79
|
fveq1d |
|
81 |
80
|
adantl |
|
82 |
16 20 21 22 52 74 75 78 81
|
sumpair |
|
83 |
34 65
|
oveq12d |
|
84 |
82 83
|
eqtrd |
|
85 |
4 84
|
mpteq2da |
|
86 |
|
prfi |
|
87 |
86
|
a1i |
|
88 |
|
eqid |
|
89 |
88
|
ax-gen |
|
90 |
|
nfcv |
|
91 |
1 90
|
nffv |
|
92 |
91 2
|
nfeq |
|
93 |
|
fveq1 |
|
94 |
93
|
a1d |
|
95 |
92 94
|
ralrimi |
|
96 |
|
mpteq12f |
|
97 |
89 95 96
|
sylancr |
|
98 |
97
|
adantl |
|
99 |
|
retopon |
|
100 |
6 99
|
eqeltri |
|
101 |
100
|
a1i |
|
102 |
|
cnf2 |
|
103 |
7 101 8 102
|
syl3anc |
|
104 |
103
|
ffnd |
|
105 |
2
|
dffn5f |
|
106 |
104 105
|
sylib |
|
107 |
106
|
adantr |
|
108 |
98 107
|
eqtr4d |
|
109 |
8
|
adantr |
|
110 |
108 109
|
eqeltrd |
|
111 |
110
|
adantlr |
|
112 |
91 3
|
nfeq |
|
113 |
|
fveq1 |
|
114 |
113
|
a1d |
|
115 |
112 114
|
ralrimi |
|
116 |
|
mpteq12f |
|
117 |
89 115 116
|
sylancr |
|
118 |
117
|
adantl |
|
119 |
|
cnf2 |
|
120 |
7 101 9 119
|
syl3anc |
|
121 |
120
|
ffnd |
|
122 |
3
|
dffn5f |
|
123 |
121 122
|
sylib |
|
124 |
123
|
adantr |
|
125 |
118 124
|
eqtr4d |
|
126 |
9
|
adantr |
|
127 |
125 126
|
eqeltrd |
|
128 |
127
|
adantlr |
|
129 |
|
simpr |
|
130 |
8 9
|
ifcld |
|
131 |
130
|
adantr |
|
132 |
5
|
fvmpt2 |
|
133 |
129 131 132
|
syl2anc |
|
134 |
|
iftrue |
|
135 |
133 134
|
sylan9eq |
|
136 |
135
|
orcd |
|
137 |
133
|
adantr |
|
138 |
|
neeq2 |
|
139 |
60 138
|
mpbiri |
|
140 |
139
|
necomd |
|
141 |
140
|
neneqd |
|
142 |
141
|
adantl |
|
143 |
142
|
iffalsed |
|
144 |
137 143
|
eqtrd |
|
145 |
144
|
olcd |
|
146 |
|
elpri |
|
147 |
146
|
adantl |
|
148 |
136 145 147
|
mpjaodan |
|
149 |
111 128 148
|
mpjaodan |
|
150 |
4 6 7 87 149
|
refsumcn |
|
151 |
85 150
|
eqeltrrd |
|