Step |
Hyp |
Ref |
Expression |
1 |
|
smfinflem.m |
|
2 |
|
smfinflem.z |
|
3 |
|
smfinflem.s |
|
4 |
|
smfinflem.f |
|
5 |
|
smfinflem.d |
|
6 |
|
smfinflem.g |
|
7 |
6
|
a1i |
|
8 |
|
nfv |
|
9 |
1 2
|
uzn0d |
|
10 |
9
|
adantr |
|
11 |
3
|
adantr |
|
12 |
4
|
ffvelrnda |
|
13 |
|
eqid |
|
14 |
11 12 13
|
smff |
|
15 |
14
|
adantlr |
|
16 |
|
ssrab2 |
|
17 |
5
|
eleq2i |
|
18 |
17
|
biimpi |
|
19 |
16 18
|
sselid |
|
20 |
19
|
adantr |
|
21 |
|
simpr |
|
22 |
|
eliinid |
|
23 |
20 21 22
|
syl2anc |
|
24 |
23
|
adantll |
|
25 |
15 24
|
ffvelrnd |
|
26 |
|
rabidim2 |
|
27 |
18 26
|
syl |
|
28 |
27
|
adantl |
|
29 |
8 10 25 28
|
infnsuprnmpt |
|
30 |
29
|
mpteq2dva |
|
31 |
7 30
|
eqtrd |
|
32 |
|
nfv |
|
33 |
|
fvex |
|
34 |
33
|
dmex |
|
35 |
34
|
rgenw |
|
36 |
35
|
a1i |
|
37 |
9 36
|
iinexd |
|
38 |
5 37
|
rabexd |
|
39 |
25
|
renegcld |
|
40 |
|
fveq2 |
|
41 |
40
|
breq2d |
|
42 |
41
|
ralbidv |
|
43 |
42
|
rexbidv |
|
44 |
|
nfcv |
|
45 |
|
nfcv |
|
46 |
|
nfcv |
|
47 |
46
|
nfdm |
|
48 |
45 47
|
nfiin |
|
49 |
|
nfv |
|
50 |
|
nfv |
|
51 |
|
nfcv |
|
52 |
|
nfcv |
|
53 |
52
|
nfdm |
|
54 |
|
fveq2 |
|
55 |
54
|
dmeqd |
|
56 |
51 53 55
|
cbviin |
|
57 |
56
|
a1i |
|
58 |
|
fveq2 |
|
59 |
58
|
breq2d |
|
60 |
59
|
ralbidv |
|
61 |
|
nfv |
|
62 |
|
nfcv |
|
63 |
|
nfcv |
|
64 |
|
nfcv |
|
65 |
52 64
|
nffv |
|
66 |
62 63 65
|
nfbr |
|
67 |
54
|
fveq1d |
|
68 |
67
|
breq2d |
|
69 |
61 66 68
|
cbvralw |
|
70 |
69
|
a1i |
|
71 |
60 70
|
bitrd |
|
72 |
71
|
rexbidv |
|
73 |
|
breq1 |
|
74 |
73
|
ralbidv |
|
75 |
74
|
cbvrexvw |
|
76 |
75
|
a1i |
|
77 |
72 76
|
bitrd |
|
78 |
44 48 49 50 57 77
|
cbvrabcsfw |
|
79 |
5 78
|
eqtri |
|
80 |
43 79
|
elrab2 |
|
81 |
80
|
biimpi |
|
82 |
81
|
simprd |
|
83 |
82
|
adantl |
|
84 |
|
renegcl |
|
85 |
84
|
ad2antlr |
|
86 |
|
fveq2 |
|
87 |
86
|
fveq1d |
|
88 |
87
|
breq2d |
|
89 |
88
|
rspcva |
|
90 |
89
|
ancoms |
|
91 |
90
|
adantll |
|
92 |
|
simpllr |
|
93 |
25
|
ad4ant14 |
|
94 |
92 93
|
lenegd |
|
95 |
91 94
|
mpbid |
|
96 |
95
|
ralrimiva |
|
97 |
|
brralrspcev |
|
98 |
85 96 97
|
syl2anc |
|
99 |
98
|
rexlimdva2 |
|
100 |
83 99
|
mpd |
|
101 |
8 10 39 100
|
suprclrnmpt |
|
102 |
5
|
a1i |
|
103 |
|
nfv |
|
104 |
|
nfv |
|
105 |
|
renegcl |
|
106 |
105
|
3ad2ant2 |
|
107 |
|
nfv |
|
108 |
|
nfcv |
|
109 |
|
nfii1 |
|
110 |
108 109
|
nfel |
|
111 |
107 110
|
nfan |
|
112 |
62
|
nfel1 |
|
113 |
|
nfra1 |
|
114 |
111 112 113
|
nf3an |
|
115 |
|
simpl2 |
|
116 |
|
simpll |
|
117 |
|
simpr |
|
118 |
22
|
adantll |
|
119 |
14
|
3adant3 |
|
120 |
|
simp3 |
|
121 |
119 120
|
ffvelrnd |
|
122 |
116 117 118 121
|
syl3anc |
|
123 |
122
|
3ad2antl1 |
|
124 |
|
rspa |
|
125 |
124
|
3ad2antl3 |
|
126 |
|
leneg |
|
127 |
126
|
biimp3a |
|
128 |
115 123 125 127
|
syl3anc |
|
129 |
128
|
ex |
|
130 |
114 129
|
ralrimi |
|
131 |
|
brralrspcev |
|
132 |
106 130 131
|
syl2anc |
|
133 |
132
|
3exp |
|
134 |
103 104 133
|
rexlimd |
|
135 |
84
|
3ad2ant2 |
|
136 |
|
nfv |
|
137 |
|
nfra1 |
|
138 |
111 136 137
|
nf3an |
|
139 |
122
|
3ad2antl1 |
|
140 |
|
simpl2 |
|
141 |
|
rspa |
|
142 |
141
|
3ad2antl3 |
|
143 |
|
simp3 |
|
144 |
|
renegcl |
|
145 |
144
|
adantr |
|
146 |
|
simpr |
|
147 |
|
leneg |
|
148 |
145 146 147
|
syl2anc |
|
149 |
148
|
3adant3 |
|
150 |
143 149
|
mpbid |
|
151 |
|
recn |
|
152 |
151
|
negnegd |
|
153 |
152
|
3ad2ant1 |
|
154 |
150 153
|
breqtrd |
|
155 |
139 140 142 154
|
syl3anc |
|
156 |
155
|
ex |
|
157 |
138 156
|
ralrimi |
|
158 |
|
breq1 |
|
159 |
158
|
ralbidv |
|
160 |
159
|
rspcev |
|
161 |
135 157 160
|
syl2anc |
|
162 |
161
|
3exp |
|
163 |
162
|
rexlimdv |
|
164 |
134 163
|
impbid |
|
165 |
32 164
|
rabbida |
|
166 |
102 165
|
eqtrd |
|
167 |
32 166
|
alrimi |
|
168 |
|
eqid |
|
169 |
168
|
rgenw |
|
170 |
169
|
a1i |
|
171 |
|
mpteq12f |
|
172 |
167 170 171
|
syl2anc |
|
173 |
|
nfv |
|
174 |
121
|
renegcld |
|
175 |
|
nfv |
|
176 |
34
|
a1i |
|
177 |
121
|
3expa |
|
178 |
14
|
feqmptd |
|
179 |
178
|
eqcomd |
|
180 |
179 12
|
eqeltrd |
|
181 |
175 11 176 177 180
|
smfneg |
|
182 |
|
eqid |
|
183 |
|
eqid |
|
184 |
107 32 173 1 2 3 174 181 182 183
|
smfsupmpt |
|
185 |
172 184
|
eqeltrd |
|
186 |
32 3 38 101 185
|
smfneg |
|
187 |
31 186
|
eqeltrd |
|