Step |
Hyp |
Ref |
Expression |
1 |
|
difelfznle |
|
2 |
1
|
3exp |
|
3 |
2
|
ad2antrr |
|
4 |
3
|
imp |
|
5 |
4
|
adantr |
|
6 |
5
|
com12 |
|
7 |
6
|
adantl |
|
8 |
7
|
imp |
|
9 |
|
simprl |
|
10 |
9
|
ad2antrr |
|
11 |
|
elfzelz |
|
12 |
11
|
adantr |
|
13 |
12
|
ad2antrr |
|
14 |
|
elfz2 |
|
15 |
|
zaddcl |
|
16 |
15
|
adantrr |
|
17 |
|
simprr |
|
18 |
16 17
|
zsubcld |
|
19 |
18
|
ex |
|
20 |
|
elfzelz |
|
21 |
19 20
|
syl11 |
|
22 |
21
|
3adant1 |
|
23 |
22
|
adantr |
|
24 |
14 23
|
sylbi |
|
25 |
24
|
ad2antrr |
|
26 |
25
|
imp |
|
27 |
|
2cshw |
|
28 |
10 13 26 27
|
syl3anc |
|
29 |
17 18
|
zaddcld |
|
30 |
29
|
ex |
|
31 |
30 20
|
syl11 |
|
32 |
31
|
3adant1 |
|
33 |
32
|
adantr |
|
34 |
14 33
|
sylbi |
|
35 |
34
|
ad2antrr |
|
36 |
35
|
imp |
|
37 |
|
cshwsublen |
|
38 |
10 36 37
|
syl2anc |
|
39 |
28 38
|
eqtrd |
|
40 |
|
elfz2nn0 |
|
41 |
|
nn0cn |
|
42 |
|
nn0cn |
|
43 |
|
nn0cn |
|
44 |
42 43
|
anim12i |
|
45 |
|
simprl |
|
46 |
|
addcl |
|
47 |
46
|
adantrl |
|
48 |
45 47
|
pncan3d |
|
49 |
48
|
oveq1d |
|
50 |
|
pncan |
|
51 |
50
|
adantrl |
|
52 |
49 51
|
eqtrd |
|
53 |
41 44 52
|
syl2an |
|
54 |
53
|
ex |
|
55 |
|
elfznn0 |
|
56 |
54 55
|
syl11 |
|
57 |
56
|
3adant3 |
|
58 |
40 57
|
sylbi |
|
59 |
58
|
adantr |
|
60 |
|
oveq2 |
|
61 |
60
|
eqeq1d |
|
62 |
61
|
imbi2d |
|
63 |
62
|
adantl |
|
64 |
63
|
adantl |
|
65 |
59 64
|
mpbird |
|
66 |
65
|
adantr |
|
67 |
66
|
imp |
|
68 |
67
|
oveq2d |
|
69 |
39 68
|
eqtr2d |
|
70 |
69
|
adantr |
|
71 |
|
oveq1 |
|
72 |
71
|
adantl |
|
73 |
70 72
|
eqtr4d |
|
74 |
73
|
exp41 |
|
75 |
74
|
com24 |
|
76 |
75
|
imp41 |
|
77 |
76
|
eqeq2d |
|
78 |
77
|
biimpd |
|
79 |
78
|
impancom |
|
80 |
79
|
impcom |
|
81 |
|
oveq2 |
|
82 |
81
|
rspceeqv |
|
83 |
8 80 82
|
syl2anc |
|
84 |
83
|
exp31 |
|
85 |
|
oveq2 |
|
86 |
85
|
eqeq2d |
|
87 |
|
cshw0 |
|
88 |
87
|
adantr |
|
89 |
88
|
eqeq2d |
|
90 |
|
fznn0sub2 |
|
91 |
90
|
adantl |
|
92 |
|
oveq1 |
|
93 |
92
|
eleq1d |
|
94 |
93
|
ad2antlr |
|
95 |
91 94
|
mpbird |
|
96 |
95
|
adantr |
|
97 |
|
oveq1 |
|
98 |
|
simpl |
|
99 |
|
2cshwid |
|
100 |
98 11 99
|
syl2an |
|
101 |
97 100
|
sylan9eqr |
|
102 |
101
|
eqcomd |
|
103 |
|
oveq2 |
|
104 |
103
|
rspceeqv |
|
105 |
96 102 104
|
syl2anc |
|
106 |
105
|
adantr |
|
107 |
|
eqeq1 |
|
108 |
107
|
rexbidv |
|
109 |
108
|
adantl |
|
110 |
106 109
|
mpbird |
|
111 |
110
|
exp41 |
|
112 |
111
|
com24 |
|
113 |
89 112
|
sylbid |
|
114 |
113
|
com24 |
|
115 |
114
|
impcom |
|
116 |
115
|
com13 |
|
117 |
116
|
a1d |
|
118 |
86 117
|
syl6bi |
|
119 |
118
|
com24 |
|
120 |
119
|
com15 |
|
121 |
120
|
imp41 |
|
122 |
121
|
com12 |
|
123 |
|
difelfzle |
|
124 |
123
|
3exp |
|
125 |
124
|
ad2antrr |
|
126 |
125
|
imp |
|
127 |
126
|
adantr |
|
128 |
127
|
impcom |
|
129 |
9
|
ad2antrr |
|
130 |
12
|
ad2antrr |
|
131 |
|
zsubcl |
|
132 |
131
|
ex |
|
133 |
20 11 132
|
syl2imc |
|
134 |
133
|
ad2antrr |
|
135 |
134
|
imp |
|
136 |
|
2cshw |
|
137 |
129 130 135 136
|
syl3anc |
|
138 |
|
zcn |
|
139 |
20
|
zcnd |
|
140 |
|
pncan3 |
|
141 |
138 139 140
|
syl2anr |
|
142 |
141
|
ex |
|
143 |
11 142
|
syl5com |
|
144 |
143
|
ad2antrr |
|
145 |
144
|
imp |
|
146 |
145
|
oveq2d |
|
147 |
137 146
|
eqtr2d |
|
148 |
147
|
adantr |
|
149 |
|
oveq1 |
|
150 |
149
|
eqeq2d |
|
151 |
150
|
adantl |
|
152 |
148 151
|
mpbird |
|
153 |
152
|
eqeq2d |
|
154 |
153
|
biimpd |
|
155 |
154
|
exp41 |
|
156 |
155
|
com24 |
|
157 |
156
|
imp31 |
|
158 |
157
|
com23 |
|
159 |
158
|
imp |
|
160 |
159
|
impcom |
|
161 |
|
oveq2 |
|
162 |
161
|
rspceeqv |
|
163 |
128 160 162
|
syl2anc |
|
164 |
163
|
ex |
|
165 |
84 122 164
|
pm2.61ii |
|
166 |
165
|
rexlimdva2 |
|
167 |
166
|
ex |
|
168 |
167
|
com23 |
|
169 |
168
|
ex |
|
170 |
169
|
com24 |
|
171 |
170
|
3imp |
|
172 |
171
|
com12 |
|