Step |
Hyp |
Ref |
Expression |
1 |
|
elnn0 |
|
2 |
|
elnn0 |
|
3 |
|
relexpaddnn |
|
4 |
3
|
a1d |
|
5 |
4
|
3exp |
|
6 |
5
|
com12 |
|
7 |
|
elnn1uz2 |
|
8 |
|
coires1 |
|
9 |
|
simpll |
|
10 |
|
simplr |
|
11 |
9 10
|
oveq12d |
|
12 |
|
1p0e1 |
|
13 |
11 12
|
eqtrdi |
|
14 |
|
simprr |
|
15 |
13 14
|
mpd |
|
16 |
9
|
oveq2d |
|
17 |
|
simprl |
|
18 |
|
relexp1g |
|
19 |
17 18
|
syl |
|
20 |
16 19
|
eqtrd |
|
21 |
20
|
releqd |
|
22 |
15 21
|
mpbird |
|
23 |
|
1nn |
|
24 |
9 23
|
eqeltrdi |
|
25 |
|
relexpnndm |
|
26 |
24 17 25
|
syl2anc |
|
27 |
|
ssun1 |
|
28 |
26 27
|
sstrdi |
|
29 |
|
relssres |
|
30 |
22 28 29
|
syl2anc |
|
31 |
8 30
|
syl5eq |
|
32 |
10
|
oveq2d |
|
33 |
|
relexp0g |
|
34 |
17 33
|
syl |
|
35 |
32 34
|
eqtrd |
|
36 |
35
|
coeq2d |
|
37 |
10
|
oveq2d |
|
38 |
|
ax-1cn |
|
39 |
9 38
|
eqeltrdi |
|
40 |
39
|
addid1d |
|
41 |
37 40
|
eqtrd |
|
42 |
41
|
oveq2d |
|
43 |
31 36 42
|
3eqtr4d |
|
44 |
43
|
exp43 |
|
45 |
|
simp1 |
|
46 |
|
simp3 |
|
47 |
|
relexpuzrel |
|
48 |
45 46 47
|
syl2anc |
|
49 |
|
eluz2nn |
|
50 |
45 49
|
syl |
|
51 |
50 46 25
|
syl2anc |
|
52 |
51 27
|
sstrdi |
|
53 |
48 52 29
|
syl2anc |
|
54 |
8 53
|
syl5eq |
|
55 |
|
simp2 |
|
56 |
55
|
oveq2d |
|
57 |
46 33
|
syl |
|
58 |
56 57
|
eqtrd |
|
59 |
58
|
coeq2d |
|
60 |
55
|
oveq2d |
|
61 |
|
eluzelcn |
|
62 |
45 61
|
syl |
|
63 |
62
|
addid1d |
|
64 |
60 63
|
eqtrd |
|
65 |
64
|
oveq2d |
|
66 |
54 59 65
|
3eqtr4d |
|
67 |
66
|
a1d |
|
68 |
67
|
3exp |
|
69 |
44 68
|
jaoi |
|
70 |
7 69
|
sylbi |
|
71 |
70
|
com12 |
|
72 |
6 71
|
jaoi |
|
73 |
2 72
|
sylbi |
|
74 |
73
|
com12 |
|
75 |
74
|
3impd |
|
76 |
|
elnn1uz2 |
|
77 |
|
coires1 |
|
78 |
|
relcnv |
|
79 |
|
ssun1 |
|
80 |
78 79
|
pm3.2i |
|
81 |
|
relssres |
|
82 |
80 81
|
mp1i |
|
83 |
77 82
|
syl5eq |
|
84 |
|
cnvco |
|
85 |
|
simplr |
|
86 |
|
1nn0 |
|
87 |
85 86
|
eqeltrdi |
|
88 |
|
simprl |
|
89 |
|
relexpcnv |
|
90 |
87 88 89
|
syl2anc |
|
91 |
85
|
oveq2d |
|
92 |
|
cnvexg |
|
93 |
88 92
|
syl |
|
94 |
|
relexp1g |
|
95 |
93 94
|
syl |
|
96 |
90 91 95
|
3eqtrd |
|
97 |
|
simpll |
|
98 |
|
0nn0 |
|
99 |
97 98
|
eqeltrdi |
|
100 |
|
relexpcnv |
|
101 |
99 88 100
|
syl2anc |
|
102 |
97
|
oveq2d |
|
103 |
|
relexp0g |
|
104 |
93 103
|
syl |
|
105 |
101 102 104
|
3eqtrd |
|
106 |
96 105
|
coeq12d |
|
107 |
84 106
|
syl5eq |
|
108 |
99 87
|
nn0addcld |
|
109 |
|
relexpcnv |
|
110 |
108 88 109
|
syl2anc |
|
111 |
97 85
|
oveq12d |
|
112 |
|
0p1e1 |
|
113 |
111 112
|
eqtrdi |
|
114 |
113
|
oveq2d |
|
115 |
110 114 95
|
3eqtrd |
|
116 |
83 107 115
|
3eqtr4d |
|
117 |
|
relco |
|
118 |
|
simprr |
|
119 |
113 118
|
mpd |
|
120 |
113
|
oveq2d |
|
121 |
88 18
|
syl |
|
122 |
120 121
|
eqtrd |
|
123 |
122
|
releqd |
|
124 |
119 123
|
mpbird |
|
125 |
|
cnveqb |
|
126 |
117 124 125
|
sylancr |
|
127 |
116 126
|
mpbird |
|
128 |
127
|
exp43 |
|
129 |
128
|
com12 |
|
130 |
|
coires1 |
|
131 |
|
simp2 |
|
132 |
|
simp3 |
|
133 |
132 92
|
syl |
|
134 |
|
relexpuzrel |
|
135 |
131 133 134
|
syl2anc |
|
136 |
|
eluz2nn |
|
137 |
131 136
|
syl |
|
138 |
|
relexpnndm |
|
139 |
137 133 138
|
syl2anc |
|
140 |
139 79
|
sstrdi |
|
141 |
|
relssres |
|
142 |
135 140 141
|
syl2anc |
|
143 |
130 142
|
syl5eq |
|
144 |
|
simp1 |
|
145 |
144
|
oveq2d |
|
146 |
133 103
|
syl |
|
147 |
145 146
|
eqtrd |
|
148 |
147
|
coeq2d |
|
149 |
144
|
oveq1d |
|
150 |
|
eluzelcn |
|
151 |
131 150
|
syl |
|
152 |
151
|
addid2d |
|
153 |
149 152
|
eqtrd |
|
154 |
153
|
oveq2d |
|
155 |
143 148 154
|
3eqtr4d |
|
156 |
|
nnnn0 |
|
157 |
131 136 156
|
3syl |
|
158 |
157 132 89
|
syl2anc |
|
159 |
144 98
|
eqeltrdi |
|
160 |
159 132 100
|
syl2anc |
|
161 |
158 160
|
coeq12d |
|
162 |
84 161
|
syl5eq |
|
163 |
159 157
|
nn0addcld |
|
164 |
163 132 109
|
syl2anc |
|
165 |
155 162 164
|
3eqtr4d |
|
166 |
159
|
nn0cnd |
|
167 |
151 166
|
addcomd |
|
168 |
|
uzaddcl |
|
169 |
131 159 168
|
syl2anc |
|
170 |
167 169
|
eqeltrrd |
|
171 |
|
relexpuzrel |
|
172 |
170 132 171
|
syl2anc |
|
173 |
117 172 125
|
sylancr |
|
174 |
165 173
|
mpbird |
|
175 |
174
|
a1d |
|
176 |
175
|
3exp |
|
177 |
176
|
com12 |
|
178 |
129 177
|
jaoi |
|
179 |
76 178
|
sylbi |
|
180 |
|
coires1 |
|
181 |
|
simp3 |
|
182 |
|
relexp0rel |
|
183 |
181 182
|
syl |
|
184 |
181 33
|
syl |
|
185 |
184
|
dmeqd |
|
186 |
|
dmresi |
|
187 |
185 186
|
eqtrdi |
|
188 |
|
eqimss |
|
189 |
187 188
|
syl |
|
190 |
|
relssres |
|
191 |
183 189 190
|
syl2anc |
|
192 |
180 191
|
syl5eq |
|
193 |
|
simp1 |
|
194 |
193
|
oveq2d |
|
195 |
|
simp2 |
|
196 |
195
|
oveq2d |
|
197 |
196 184
|
eqtrd |
|
198 |
194 197
|
coeq12d |
|
199 |
193 195
|
oveq12d |
|
200 |
|
00id |
|
201 |
199 200
|
eqtrdi |
|
202 |
201
|
oveq2d |
|
203 |
192 198 202
|
3eqtr4d |
|
204 |
203
|
a1d |
|
205 |
204
|
3exp |
|
206 |
205
|
com12 |
|
207 |
179 206
|
jaoi |
|
208 |
2 207
|
sylbi |
|
209 |
208
|
com12 |
|
210 |
209
|
3impd |
|
211 |
75 210
|
jaoi |
|
212 |
1 211
|
sylbi |
|
213 |
212
|
imp |
|