Step |
Hyp |
Ref |
Expression |
1 |
|
efgval.w |
|
2 |
|
efgval.r |
|
3 |
|
efgval2.m |
|
4 |
|
efgval2.t |
|
5 |
|
efgred.d |
|
6 |
|
efgred.s |
|
7 |
|
efgcpbllem.1 |
|
8 |
1 2 3 4
|
efgval2 |
|
9 |
7
|
relopabi |
|
10 |
9
|
a1i |
|
11 |
1 2 3 4 5 6 7
|
efgcpbllema |
|
12 |
11
|
simp2bi |
|
13 |
12
|
adantl |
|
14 |
11
|
simp1bi |
|
15 |
14
|
adantl |
|
16 |
1 2
|
efger |
|
17 |
16
|
a1i |
|
18 |
11
|
simp3bi |
|
19 |
18
|
adantl |
|
20 |
17 19
|
ersym |
|
21 |
1 2 3 4 5 6 7
|
efgcpbllema |
|
22 |
13 15 20 21
|
syl3anbrc |
|
23 |
14
|
ad2antrl |
|
24 |
1 2 3 4 5 6 7
|
efgcpbllema |
|
25 |
24
|
simp2bi |
|
26 |
25
|
ad2antll |
|
27 |
16
|
a1i |
|
28 |
18
|
ad2antrl |
|
29 |
24
|
simp3bi |
|
30 |
29
|
ad2antll |
|
31 |
27 28 30
|
ertrd |
|
32 |
1 2 3 4 5 6 7
|
efgcpbllema |
|
33 |
23 26 31 32
|
syl3anbrc |
|
34 |
16
|
a1i |
|
35 |
|
fviss |
|
36 |
1 35
|
eqsstri |
|
37 |
|
simpll |
|
38 |
36 37
|
sseldi |
|
39 |
|
simpr |
|
40 |
36 39
|
sseldi |
|
41 |
|
ccatcl |
|
42 |
38 40 41
|
syl2anc |
|
43 |
|
simplr |
|
44 |
36 43
|
sseldi |
|
45 |
|
ccatcl |
|
46 |
42 44 45
|
syl2anc |
|
47 |
1
|
efgrcl |
|
48 |
47
|
simprd |
|
49 |
48
|
ad2antrr |
|
50 |
46 49
|
eleqtrrd |
|
51 |
34 50
|
erref |
|
52 |
51
|
ex |
|
53 |
52
|
pm4.71d |
|
54 |
1 2 3 4 5 6 7
|
efgcpbllema |
|
55 |
|
df-3an |
|
56 |
|
anidm |
|
57 |
56
|
anbi1i |
|
58 |
54 55 57
|
3bitri |
|
59 |
53 58
|
bitr4di |
|
60 |
10 22 33 59
|
iserd |
|
61 |
1 2 3 4
|
efgtf |
|
62 |
61
|
simprd |
|
63 |
62
|
adantl |
|
64 |
|
ffn |
|
65 |
|
ovelrn |
|
66 |
63 64 65
|
3syl |
|
67 |
|
simplr |
|
68 |
62
|
ad2antlr |
|
69 |
|
simprl |
|
70 |
|
simprr |
|
71 |
68 69 70
|
fovrnd |
|
72 |
50
|
adantr |
|
73 |
37
|
adantr |
|
74 |
36 73
|
sseldi |
|
75 |
40
|
adantr |
|
76 |
|
pfxcl |
|
77 |
75 76
|
syl |
|
78 |
|
ccatcl |
|
79 |
74 77 78
|
syl2anc |
|
80 |
3
|
efgmf |
|
81 |
80
|
ffvelrni |
|
82 |
81
|
ad2antll |
|
83 |
70 82
|
s2cld |
|
84 |
|
ccatcl |
|
85 |
79 83 84
|
syl2anc |
|
86 |
|
swrdcl |
|
87 |
75 86
|
syl |
|
88 |
44
|
adantr |
|
89 |
|
ccatass |
|
90 |
85 87 88 89
|
syl3anc |
|
91 |
|
ccatcl |
|
92 |
77 83 91
|
syl2anc |
|
93 |
|
ccatass |
|
94 |
74 92 87 93
|
syl3anc |
|
95 |
|
ccatass |
|
96 |
74 77 83 95
|
syl3anc |
|
97 |
96
|
oveq1d |
|
98 |
1 2 3 4
|
efgtval |
|
99 |
67 69 70 98
|
syl3anc |
|
100 |
|
splval |
|
101 |
67 69 69 83 100
|
syl13anc |
|
102 |
99 101
|
eqtrd |
|
103 |
102
|
oveq2d |
|
104 |
94 97 103
|
3eqtr4rd |
|
105 |
104
|
oveq1d |
|
106 |
|
lencl |
|
107 |
74 106
|
syl |
|
108 |
|
nn0uz |
|
109 |
107 108
|
eleqtrdi |
|
110 |
|
elfznn0 |
|
111 |
110
|
ad2antrl |
|
112 |
|
uzaddcl |
|
113 |
109 111 112
|
syl2anc |
|
114 |
42
|
adantr |
|
115 |
|
ccatlen |
|
116 |
114 88 115
|
syl2anc |
|
117 |
|
ccatlen |
|
118 |
74 75 117
|
syl2anc |
|
119 |
|
elfzuz3 |
|
120 |
119
|
ad2antrl |
|
121 |
107
|
nn0zd |
|
122 |
|
eluzadd |
|
123 |
120 121 122
|
syl2anc |
|
124 |
|
lencl |
|
125 |
75 124
|
syl |
|
126 |
125
|
nn0cnd |
|
127 |
107
|
nn0cnd |
|
128 |
126 127
|
addcomd |
|
129 |
111
|
nn0cnd |
|
130 |
129 127
|
addcomd |
|
131 |
130
|
fveq2d |
|
132 |
123 128 131
|
3eltr3d |
|
133 |
118 132
|
eqeltrd |
|
134 |
|
lencl |
|
135 |
88 134
|
syl |
|
136 |
|
uzaddcl |
|
137 |
133 135 136
|
syl2anc |
|
138 |
116 137
|
eqeltrd |
|
139 |
|
elfzuzb |
|
140 |
113 138 139
|
sylanbrc |
|
141 |
1 2 3 4
|
efgtval |
|
142 |
72 140 70 141
|
syl3anc |
|
143 |
|
wrd0 |
|
144 |
143
|
a1i |
|
145 |
|
ccatcl |
|
146 |
87 88 145
|
syl2anc |
|
147 |
|
ccatrid |
|
148 |
79 147
|
syl |
|
149 |
148
|
oveq1d |
|
150 |
|
ccatass |
|
151 |
79 87 88 150
|
syl3anc |
|
152 |
|
ccatass |
|
153 |
74 77 87 152
|
syl3anc |
|
154 |
125 108
|
eleqtrdi |
|
155 |
|
eluzfz2 |
|
156 |
154 155
|
syl |
|
157 |
|
ccatpfx |
|
158 |
75 69 156 157
|
syl3anc |
|
159 |
|
pfxid |
|
160 |
75 159
|
syl |
|
161 |
158 160
|
eqtrd |
|
162 |
161
|
oveq2d |
|
163 |
153 162
|
eqtrd |
|
164 |
163
|
oveq1d |
|
165 |
149 151 164
|
3eqtr2rd |
|
166 |
|
ccatlen |
|
167 |
74 77 166
|
syl2anc |
|
168 |
|
pfxlen |
|
169 |
75 69 168
|
syl2anc |
|
170 |
169
|
oveq2d |
|
171 |
167 170
|
eqtr2d |
|
172 |
|
hash0 |
|
173 |
172
|
oveq2i |
|
174 |
107 111
|
nn0addcld |
|
175 |
174
|
nn0cnd |
|
176 |
175
|
addid1d |
|
177 |
173 176
|
syl5req |
|
178 |
79 144 146 83 165 171 177
|
splval2 |
|
179 |
142 178
|
eqtrd |
|
180 |
90 105 179
|
3eqtr4d |
|
181 |
1 2 3 4
|
efgtf |
|
182 |
181
|
simprd |
|
183 |
|
ffn |
|
184 |
72 182 183
|
3syl |
|
185 |
|
fnovrn |
|
186 |
184 140 70 185
|
syl3anc |
|
187 |
180 186
|
eqeltrd |
|
188 |
1 2 3 4
|
efgi2 |
|
189 |
72 187 188
|
syl2anc |
|
190 |
1 2 3 4 5 6 7
|
efgcpbllema |
|
191 |
67 71 189 190
|
syl3anbrc |
|
192 |
|
vex |
|
193 |
|
vex |
|
194 |
192 193
|
elec |
|
195 |
|
breq2 |
|
196 |
194 195
|
syl5bb |
|
197 |
191 196
|
syl5ibrcom |
|
198 |
197
|
rexlimdvva |
|
199 |
66 198
|
sylbid |
|
200 |
199
|
ssrdv |
|
201 |
200
|
ralrimiva |
|
202 |
1
|
fvexi |
|
203 |
|
erex |
|
204 |
60 202 203
|
mpisyl |
|
205 |
|
ereq1 |
|
206 |
|
eceq2 |
|
207 |
206
|
sseq2d |
|
208 |
207
|
ralbidv |
|
209 |
205 208
|
anbi12d |
|
210 |
209
|
elabg |
|
211 |
204 210
|
syl |
|
212 |
60 201 211
|
mpbir2and |
|
213 |
|
intss1 |
|
214 |
212 213
|
syl |
|
215 |
8 214
|
eqsstrid |
|