Step |
Hyp |
Ref |
Expression |
1 |
|
wwlksnextbij0.v |
|
2 |
|
wwlksnextbij0.e |
|
3 |
|
wwlksnextbij0.d |
|
4 |
|
wwlksnextbij0.r |
|
5 |
|
wwlksnextbij0.f |
|
6 |
1 2 3 4 5
|
wwlksnextfun |
|
7 |
|
fveq2 |
|
8 |
|
fvex |
|
9 |
7 5 8
|
fvmpt |
|
10 |
|
fveq2 |
|
11 |
|
fvex |
|
12 |
10 5 11
|
fvmpt |
|
13 |
9 12
|
eqeqan12d |
|
14 |
13
|
adantl |
|
15 |
|
fveqeq2 |
|
16 |
|
oveq1 |
|
17 |
16
|
eqeq1d |
|
18 |
|
fveq2 |
|
19 |
18
|
preq2d |
|
20 |
19
|
eleq1d |
|
21 |
15 17 20
|
3anbi123d |
|
22 |
21 3
|
elrab2 |
|
23 |
|
fveqeq2 |
|
24 |
|
oveq1 |
|
25 |
24
|
eqeq1d |
|
26 |
|
fveq2 |
|
27 |
26
|
preq2d |
|
28 |
27
|
eleq1d |
|
29 |
23 25 28
|
3anbi123d |
|
30 |
29 3
|
elrab2 |
|
31 |
|
eqtr3 |
|
32 |
31
|
expcom |
|
33 |
32
|
3ad2ant1 |
|
34 |
33
|
adantl |
|
35 |
34
|
com12 |
|
36 |
35
|
3ad2ant1 |
|
37 |
36
|
adantl |
|
38 |
37
|
imp |
|
39 |
38
|
adantr |
|
40 |
39
|
adantr |
|
41 |
|
simpr |
|
42 |
|
eqtr3 |
|
43 |
|
1e2m1 |
|
44 |
43
|
a1i |
|
45 |
44
|
oveq2d |
|
46 |
|
nn0cn |
|
47 |
|
2cnd |
|
48 |
|
1cnd |
|
49 |
46 47 48
|
addsubassd |
|
50 |
45 49
|
eqtr4d |
|
51 |
50
|
adantr |
|
52 |
|
oveq1 |
|
53 |
52
|
eqeq2d |
|
54 |
53
|
adantl |
|
55 |
51 54
|
mpbird |
|
56 |
|
oveq2 |
|
57 |
|
oveq2 |
|
58 |
56 57
|
eqeq12d |
|
59 |
55 58
|
syl |
|
60 |
59
|
biimpd |
|
61 |
60
|
ex |
|
62 |
61
|
com13 |
|
63 |
42 62
|
syl |
|
64 |
63
|
ex |
|
65 |
64
|
com23 |
|
66 |
65
|
impcom |
|
67 |
66
|
com12 |
|
68 |
67
|
3ad2ant2 |
|
69 |
68
|
adantl |
|
70 |
69
|
com12 |
|
71 |
70
|
3adant3 |
|
72 |
71
|
adantl |
|
73 |
72
|
imp31 |
|
74 |
73
|
adantr |
|
75 |
|
simpl |
|
76 |
|
simpl |
|
77 |
75 76
|
anim12i |
|
78 |
77
|
adantr |
|
79 |
|
nn0re |
|
80 |
|
2re |
|
81 |
80
|
a1i |
|
82 |
|
nn0ge0 |
|
83 |
|
2pos |
|
84 |
83
|
a1i |
|
85 |
79 81 82 84
|
addgegt0d |
|
86 |
85
|
adantl |
|
87 |
|
breq2 |
|
88 |
87
|
adantr |
|
89 |
86 88
|
mpbird |
|
90 |
|
hashgt0n0 |
|
91 |
89 90
|
sylan2 |
|
92 |
91
|
exp32 |
|
93 |
92
|
com12 |
|
94 |
93
|
3ad2ant1 |
|
95 |
94
|
impcom |
|
96 |
95
|
adantr |
|
97 |
96
|
imp |
|
98 |
85
|
adantl |
|
99 |
|
breq2 |
|
100 |
99
|
adantr |
|
101 |
98 100
|
mpbird |
|
102 |
|
hashgt0n0 |
|
103 |
101 102
|
sylan2 |
|
104 |
103
|
exp32 |
|
105 |
104
|
com12 |
|
106 |
105
|
3ad2ant1 |
|
107 |
106
|
impcom |
|
108 |
107
|
adantl |
|
109 |
108
|
imp |
|
110 |
78 97 109
|
jca32 |
|
111 |
110
|
adantr |
|
112 |
|
simpl |
|
113 |
112
|
adantr |
|
114 |
|
simpr |
|
115 |
114
|
adantr |
|
116 |
|
hashneq0 |
|
117 |
116
|
biimprd |
|
118 |
117
|
adantr |
|
119 |
118
|
com12 |
|
120 |
119
|
adantr |
|
121 |
120
|
impcom |
|
122 |
|
pfxsuff1eqwrdeq |
|
123 |
113 115 121 122
|
syl3anc |
|
124 |
|
ancom |
|
125 |
124
|
anbi2i |
|
126 |
|
3anass |
|
127 |
125 126
|
bitr4i |
|
128 |
123 127
|
syl6bb |
|
129 |
111 128
|
syl |
|
130 |
40 41 74 129
|
mpbir3and |
|
131 |
130
|
exp31 |
|
132 |
22 30 131
|
syl2anb |
|
133 |
132
|
impcom |
|
134 |
14 133
|
sylbid |
|
135 |
134
|
ralrimivva |
|
136 |
|
dff13 |
|
137 |
6 135 136
|
sylanbrc |
|