Step |
Hyp |
Ref |
Expression |
1 |
|
rolle.a |
|
2 |
|
rolle.b |
|
3 |
|
rolle.lt |
|
4 |
|
rolle.f |
|
5 |
|
rolle.d |
|
6 |
|
rolle.e |
|
7 |
1 2 3
|
ltled |
|
8 |
1 2 7 4
|
evthicc |
|
9 |
|
reeanv |
|
10 |
8 9
|
sylibr |
|
11 |
|
r19.26 |
|
12 |
1
|
ad2antrr |
|
13 |
2
|
ad2antrr |
|
14 |
3
|
ad2antrr |
|
15 |
4
|
ad2antrr |
|
16 |
5
|
ad2antrr |
|
17 |
|
simpl |
|
18 |
17
|
ralimi |
|
19 |
|
fveq2 |
|
20 |
19
|
breq1d |
|
21 |
20
|
cbvralvw |
|
22 |
18 21
|
sylib |
|
23 |
22
|
ad2antrl |
|
24 |
|
simplrl |
|
25 |
|
simprr |
|
26 |
12 13 14 15 16 23 24 25
|
rollelem |
|
27 |
26
|
expr |
|
28 |
1
|
ad2antrr |
|
29 |
2
|
ad2antrr |
|
30 |
3
|
ad2antrr |
|
31 |
|
cncff |
|
32 |
4 31
|
syl |
|
33 |
32
|
ffvelrnda |
|
34 |
33
|
renegcld |
|
35 |
34
|
fmpttd |
|
36 |
|
ax-resscn |
|
37 |
|
ssid |
|
38 |
|
cncfss |
|
39 |
36 37 38
|
mp2an |
|
40 |
39 4
|
sseldi |
|
41 |
|
eqid |
|
42 |
41
|
negfcncf |
|
43 |
40 42
|
syl |
|
44 |
|
cncffvrn |
|
45 |
36 43 44
|
sylancr |
|
46 |
35 45
|
mpbird |
|
47 |
46
|
ad2antrr |
|
48 |
36
|
a1i |
|
49 |
|
iccssre |
|
50 |
1 2 49
|
syl2anc |
|
51 |
|
fss |
|
52 |
32 36 51
|
sylancl |
|
53 |
52
|
ffvelrnda |
|
54 |
53
|
negcld |
|
55 |
|
eqid |
|
56 |
55
|
tgioo2 |
|
57 |
|
iccntr |
|
58 |
1 2 57
|
syl2anc |
|
59 |
48 50 54 56 55 58
|
dvmptntr |
|
60 |
|
reelprrecn |
|
61 |
60
|
a1i |
|
62 |
|
ioossicc |
|
63 |
62
|
sseli |
|
64 |
63 53
|
sylan2 |
|
65 |
|
fvexd |
|
66 |
32
|
feqmptd |
|
67 |
66
|
oveq2d |
|
68 |
|
dvf |
|
69 |
5
|
feq2d |
|
70 |
68 69
|
mpbii |
|
71 |
70
|
feqmptd |
|
72 |
48 50 53 56 55 58
|
dvmptntr |
|
73 |
67 71 72
|
3eqtr3rd |
|
74 |
61 64 65 73
|
dvmptneg |
|
75 |
59 74
|
eqtrd |
|
76 |
75
|
dmeqd |
|
77 |
|
dmmptg |
|
78 |
|
negex |
|
79 |
78
|
a1i |
|
80 |
77 79
|
mprg |
|
81 |
76 80
|
eqtrdi |
|
82 |
81
|
ad2antrr |
|
83 |
|
simpr |
|
84 |
32
|
ad2antrr |
|
85 |
|
simplrr |
|
86 |
84 85
|
ffvelrnd |
|
87 |
32
|
adantr |
|
88 |
87
|
ffvelrnda |
|
89 |
86 88
|
lenegd |
|
90 |
|
fveq2 |
|
91 |
90
|
negeqd |
|
92 |
|
negex |
|
93 |
91 41 92
|
fvmpt |
|
94 |
93
|
adantl |
|
95 |
|
fveq2 |
|
96 |
95
|
negeqd |
|
97 |
|
negex |
|
98 |
96 41 97
|
fvmpt |
|
99 |
85 98
|
syl |
|
100 |
94 99
|
breq12d |
|
101 |
89 100
|
bitr4d |
|
102 |
83 101
|
syl5ib |
|
103 |
102
|
ralimdva |
|
104 |
103
|
imp |
|
105 |
|
fveq2 |
|
106 |
105
|
breq1d |
|
107 |
106
|
cbvralvw |
|
108 |
104 107
|
sylib |
|
109 |
108
|
adantrr |
|
110 |
|
simplrr |
|
111 |
|
simprr |
|
112 |
28 29 30 47 82 109 110 111
|
rollelem |
|
113 |
75
|
fveq1d |
|
114 |
|
fveq2 |
|
115 |
114
|
negeqd |
|
116 |
|
eqid |
|
117 |
|
negex |
|
118 |
115 116 117
|
fvmpt |
|
119 |
113 118
|
sylan9eq |
|
120 |
119
|
eqeq1d |
|
121 |
5
|
eleq2d |
|
122 |
121
|
biimpar |
|
123 |
68
|
ffvelrni |
|
124 |
122 123
|
syl |
|
125 |
124
|
negeq0d |
|
126 |
120 125
|
bitr4d |
|
127 |
126
|
rexbidva |
|
128 |
127
|
ad2antrr |
|
129 |
112 128
|
mpbid |
|
130 |
129
|
expr |
|
131 |
|
vex |
|
132 |
131
|
elpr |
|
133 |
|
fveq2 |
|
134 |
133
|
a1i |
|
135 |
6
|
eqcomd |
|
136 |
|
fveqeq2 |
|
137 |
135 136
|
syl5ibrcom |
|
138 |
134 137
|
jaod |
|
139 |
132 138
|
syl5bi |
|
140 |
|
eleq1w |
|
141 |
|
fveqeq2 |
|
142 |
140 141
|
imbi12d |
|
143 |
142
|
imbi2d |
|
144 |
143 139
|
chvarvv |
|
145 |
139 144
|
anim12d |
|
146 |
145
|
ad2antrr |
|
147 |
1
|
rexrd |
|
148 |
2
|
rexrd |
|
149 |
|
lbicc2 |
|
150 |
147 148 7 149
|
syl3anc |
|
151 |
32 150
|
ffvelrnd |
|
152 |
151
|
ad2antrr |
|
153 |
88 152
|
letri3d |
|
154 |
|
breq2 |
|
155 |
|
breq1 |
|
156 |
154 155
|
bi2anan9 |
|
157 |
156
|
bibi2d |
|
158 |
153 157
|
syl5ibrcom |
|
159 |
158
|
impancom |
|
160 |
159
|
imp |
|
161 |
160
|
ralbidva |
|
162 |
32
|
ffnd |
|
163 |
|
fnconstg |
|
164 |
151 163
|
syl |
|
165 |
|
eqfnfv |
|
166 |
162 164 165
|
syl2anc |
|
167 |
|
fvex |
|
168 |
167
|
fvconst2 |
|
169 |
168
|
eqeq2d |
|
170 |
169
|
ralbiia |
|
171 |
166 170
|
bitrdi |
|
172 |
|
ioon0 |
|
173 |
147 148 172
|
syl2anc |
|
174 |
3 173
|
mpbird |
|
175 |
|
fconstmpt |
|
176 |
175
|
eqeq2i |
|
177 |
176
|
biimpi |
|
178 |
177
|
oveq2d |
|
179 |
151
|
recnd |
|
180 |
179
|
adantr |
|
181 |
|
0cnd |
|
182 |
61 179
|
dvmptc |
|
183 |
61 180 181 182 50 56 55 58
|
dvmptres2 |
|
184 |
178 183
|
sylan9eqr |
|
185 |
184
|
fveq1d |
|
186 |
|
eqidd |
|
187 |
|
eqid |
|
188 |
|
c0ex |
|
189 |
186 187 188
|
fvmpt |
|
190 |
185 189
|
sylan9eq |
|
191 |
190
|
ralrimiva |
|
192 |
|
r19.2z |
|
193 |
174 191 192
|
syl2an2r |
|
194 |
193
|
ex |
|
195 |
171 194
|
sylbird |
|
196 |
195
|
ad2antrr |
|
197 |
161 196
|
sylbird |
|
198 |
197
|
impancom |
|
199 |
146 198
|
syld |
|
200 |
27 130 199
|
ecased |
|
201 |
200
|
ex |
|
202 |
11 201
|
syl5bir |
|
203 |
202
|
rexlimdvva |
|
204 |
10 203
|
mpd |
|