Step |
Hyp |
Ref |
Expression |
1 |
|
clwwlkext2edg.v |
|
2 |
|
clwwlkext2edg.e |
|
3 |
|
wwlknbp1 |
|
4 |
1
|
wrdeqi |
|
5 |
4
|
eleq2i |
|
6 |
5
|
biimpri |
|
7 |
6
|
3ad2ant2 |
|
8 |
7
|
ad2antlr |
|
9 |
|
s1cl |
|
10 |
9
|
adantl |
|
11 |
|
ccatcl |
|
12 |
8 10 11
|
syl2anc |
|
13 |
12
|
adantr |
|
14 |
1 2
|
wwlknp |
|
15 |
|
simplll |
|
16 |
9
|
adantr |
|
17 |
16
|
ad2antlr |
|
18 |
|
elfzo0 |
|
19 |
|
simp1 |
|
20 |
|
peano2nn |
|
21 |
20
|
3ad2ant2 |
|
22 |
|
nn0re |
|
23 |
22
|
3ad2ant1 |
|
24 |
|
nnre |
|
25 |
24
|
3ad2ant2 |
|
26 |
|
peano2re |
|
27 |
24 26
|
syl |
|
28 |
27
|
3ad2ant2 |
|
29 |
|
simp3 |
|
30 |
24
|
ltp1d |
|
31 |
30
|
3ad2ant2 |
|
32 |
23 25 28 29 31
|
lttrd |
|
33 |
|
elfzo0 |
|
34 |
19 21 32 33
|
syl3anbrc |
|
35 |
18 34
|
sylbi |
|
36 |
35
|
adantl |
|
37 |
|
oveq2 |
|
38 |
37
|
adantl |
|
39 |
38
|
eleq2d |
|
40 |
39
|
ad2antrr |
|
41 |
36 40
|
mpbird |
|
42 |
|
ccatval1 |
|
43 |
15 17 41 42
|
syl3anc |
|
44 |
|
fzonn0p1p1 |
|
45 |
44
|
adantl |
|
46 |
37
|
eleq2d |
|
47 |
46
|
ad3antlr |
|
48 |
45 47
|
mpbird |
|
49 |
|
ccatval1 |
|
50 |
15 17 48 49
|
syl3anc |
|
51 |
43 50
|
preq12d |
|
52 |
51
|
ex |
|
53 |
52
|
expcom |
|
54 |
53
|
expcom |
|
55 |
54
|
3ad2ant1 |
|
56 |
55
|
imp |
|
57 |
56
|
expdcom |
|
58 |
57
|
3imp1 |
|
59 |
58
|
eleq1d |
|
60 |
59
|
ralbidva |
|
61 |
60
|
biimprd |
|
62 |
61
|
3exp |
|
63 |
62
|
com34 |
|
64 |
63
|
3imp1 |
|
65 |
64
|
adantr |
|
66 |
|
simpll |
|
67 |
9
|
ad2antrl |
|
68 |
|
nn0p1gt0 |
|
69 |
68
|
ad2antll |
|
70 |
|
breq2 |
|
71 |
70
|
ad2antlr |
|
72 |
69 71
|
mpbird |
|
73 |
|
hashneq0 |
|
74 |
73
|
ad2antrr |
|
75 |
72 74
|
mpbid |
|
76 |
|
ccatval1lsw |
|
77 |
66 67 75 76
|
syl3anc |
|
78 |
|
oveq1 |
|
79 |
78
|
ad2antlr |
|
80 |
|
nn0cn |
|
81 |
80
|
ad2antll |
|
82 |
|
pncan1 |
|
83 |
81 82
|
syl |
|
84 |
79 83
|
eqtrd |
|
85 |
84
|
fveq2d |
|
86 |
77 85
|
eqtr3d |
|
87 |
|
ccatws1ls |
|
88 |
87
|
ad2ant2r |
|
89 |
|
fveq2 |
|
90 |
89
|
ad2antlr |
|
91 |
88 90
|
eqtr3d |
|
92 |
86 91
|
preq12d |
|
93 |
92
|
expcom |
|
94 |
93
|
expcom |
|
95 |
94
|
3ad2ant1 |
|
96 |
95
|
imp |
|
97 |
96
|
com12 |
|
98 |
97
|
3adant3 |
|
99 |
98
|
imp |
|
100 |
99
|
eleq1d |
|
101 |
100
|
biimpa |
|
102 |
|
simprl1 |
|
103 |
102
|
adantr |
|
104 |
|
fveq2 |
|
105 |
|
fvoveq1 |
|
106 |
104 105
|
preq12d |
|
107 |
106
|
eleq1d |
|
108 |
107
|
ralsng |
|
109 |
103 108
|
syl |
|
110 |
101 109
|
mpbird |
|
111 |
|
ralunb |
|
112 |
65 110 111
|
sylanbrc |
|
113 |
|
elnn0uz |
|
114 |
102 113
|
sylib |
|
115 |
114
|
adantr |
|
116 |
|
fzosplitsn |
|
117 |
115 116
|
syl |
|
118 |
117
|
raleqdv |
|
119 |
112 118
|
mpbird |
|
120 |
|
ccatws1len |
|
121 |
120
|
3ad2ant1 |
|
122 |
121
|
ad2antrr |
|
123 |
122
|
oveq1d |
|
124 |
|
oveq1 |
|
125 |
124
|
oveq1d |
|
126 |
|
1cnd |
|
127 |
80 126
|
addcld |
|
128 |
127 126
|
pncand |
|
129 |
128
|
3ad2ant1 |
|
130 |
129
|
adantr |
|
131 |
125 130
|
sylan9eq |
|
132 |
131
|
3ad2antl2 |
|
133 |
132
|
adantr |
|
134 |
123 133
|
eqtrd |
|
135 |
134
|
oveq2d |
|
136 |
135
|
raleqdv |
|
137 |
119 136
|
mpbird |
|
138 |
137
|
exp42 |
|
139 |
14 138
|
syl |
|
140 |
139
|
imp41 |
|
141 |
140
|
adantrr |
|
142 |
|
lswccats1 |
|
143 |
8 142
|
sylancom |
|
144 |
68
|
3ad2ant1 |
|
145 |
70
|
3ad2ant3 |
|
146 |
144 145
|
mpbird |
|
147 |
146
|
ad2antlr |
|
148 |
|
ccatfv0 |
|
149 |
8 10 147 148
|
syl3anc |
|
150 |
143 149
|
preq12d |
|
151 |
150
|
eleq1d |
|
152 |
151
|
biimprcd |
|
153 |
152
|
adantl |
|
154 |
153
|
impcom |
|
155 |
13 141 154
|
3jca |
|
156 |
|
ccatws1len |
|
157 |
156
|
3ad2ant2 |
|
158 |
124
|
3ad2ant3 |
|
159 |
80 126 126
|
addassd |
|
160 |
|
1p1e2 |
|
161 |
160
|
oveq2i |
|
162 |
159 161
|
eqtrdi |
|
163 |
162
|
3ad2ant1 |
|
164 |
157 158 163
|
3eqtrd |
|
165 |
164
|
ad3antlr |
|
166 |
|
2nn |
|
167 |
|
nn0nnaddcl |
|
168 |
166 167
|
mpan2 |
|
169 |
168
|
3ad2ant1 |
|
170 |
1 2
|
isclwwlknx |
|
171 |
169 170
|
syl |
|
172 |
171
|
ad3antlr |
|
173 |
155 165 172
|
mpbir2and |
|
174 |
173
|
exp31 |
|
175 |
3 174
|
mpdan |
|
176 |
175
|
imp |
|