Step |
Hyp |
Ref |
Expression |
1 |
|
vonioolem1.x |
|
2 |
|
vonioolem1.a |
|
3 |
|
vonioolem1.b |
|
4 |
|
vonioolem1.u |
|
5 |
|
vonioolem1.t |
|
6 |
|
vonioolem1.c |
|
7 |
|
vonioolem1.d |
|
8 |
|
vonioolem1.s |
|
9 |
|
vonioolem1.r |
|
10 |
|
vonioolem1.e |
|
11 |
|
vonioolem1.n |
|
12 |
|
vonioolem1.z |
|
13 |
9
|
a1i |
|
14 |
6
|
a1i |
|
15 |
1
|
mptexd |
|
16 |
15
|
adantr |
|
17 |
14 16
|
fvmpt2d |
|
18 |
|
ovexd |
|
19 |
17 18
|
fvmpt2d |
|
20 |
19
|
oveq2d |
|
21 |
3
|
ffvelrnda |
|
22 |
21
|
adantlr |
|
23 |
22
|
recnd |
|
24 |
2
|
adantr |
|
25 |
24
|
ffvelrnda |
|
26 |
25
|
recnd |
|
27 |
|
nnrecre |
|
28 |
27
|
ad2antlr |
|
29 |
28
|
recnd |
|
30 |
23 26 29
|
subsub4d |
|
31 |
20 30
|
eqtr4d |
|
32 |
31
|
prodeq2dv |
|
33 |
32
|
mpteq2dva |
|
34 |
13 33
|
eqtrd |
|
35 |
|
nfv |
|
36 |
|
rpssre |
|
37 |
2
|
ffvelrnda |
|
38 |
|
difrp |
|
39 |
37 21 38
|
syl2anc |
|
40 |
5 39
|
mpbid |
|
41 |
36 40
|
sseldi |
|
42 |
41
|
recnd |
|
43 |
|
eqid |
|
44 |
35 1 42 43
|
fprodsubrecnncnv |
|
45 |
34 44
|
eqbrtrd |
|
46 |
|
nnex |
|
47 |
46
|
mptex |
|
48 |
47
|
a1i |
|
49 |
9 48
|
eqeltrid |
|
50 |
46
|
mptex |
|
51 |
50
|
a1i |
|
52 |
8 51
|
eqeltrid |
|
53 |
|
1rp |
|
54 |
53
|
a1i |
|
55 |
|
eqid |
|
56 |
35 55 40
|
rnmptssd |
|
57 |
|
ltso |
|
58 |
57
|
a1i |
|
59 |
55
|
rnmptfi |
|
60 |
1 59
|
syl |
|
61 |
35 40 55 4
|
rnmptn0 |
|
62 |
36
|
a1i |
|
63 |
56 62
|
sstrd |
|
64 |
|
fiinfcl |
|
65 |
58 60 61 63 64
|
syl13anc |
|
66 |
10 65
|
eqeltrid |
|
67 |
56 66
|
sseldd |
|
68 |
54 67
|
rpdivcld |
|
69 |
68
|
rpred |
|
70 |
68
|
rpge0d |
|
71 |
|
flge0nn0 |
|
72 |
69 70 71
|
syl2anc |
|
73 |
|
nn0p1nn |
|
74 |
72 73
|
syl |
|
75 |
74
|
nnzd |
|
76 |
11 75
|
eqeltrid |
|
77 |
11
|
recnnltrp |
|
78 |
67 77
|
syl |
|
79 |
78
|
simpld |
|
80 |
|
uznnssnn |
|
81 |
79 80
|
syl |
|
82 |
12 81
|
eqsstrid |
|
83 |
82
|
adantr |
|
84 |
|
simpr |
|
85 |
83 84
|
sseldd |
|
86 |
7
|
a1i |
|
87 |
1
|
adantr |
|
88 |
|
eqid |
|
89 |
25 28
|
readdcld |
|
90 |
89
|
fmpttd |
|
91 |
17
|
feq1d |
|
92 |
90 91
|
mpbird |
|
93 |
3
|
adantr |
|
94 |
87 88 92 93
|
hoimbl |
|
95 |
94
|
elexd |
|
96 |
86 95
|
fvmpt2d |
|
97 |
85 96
|
syldan |
|
98 |
97
|
fveq2d |
|
99 |
1
|
adantr |
|
100 |
4
|
adantr |
|
101 |
85 92
|
syldan |
|
102 |
3
|
adantr |
|
103 |
|
eqid |
|
104 |
99 100 101 102 103
|
vonn0hoi |
|
105 |
101
|
ffvelrnda |
|
106 |
85 22
|
syldanl |
|
107 |
|
volico |
|
108 |
105 106 107
|
syl2anc |
|
109 |
85 19
|
syldanl |
|
110 |
85 28
|
syldanl |
|
111 |
79
|
nnrecred |
|
112 |
111
|
ad2antrr |
|
113 |
41
|
adantlr |
|
114 |
12
|
eleq2i |
|
115 |
114
|
biimpi |
|
116 |
|
eluzle |
|
117 |
115 116
|
syl |
|
118 |
117
|
adantl |
|
119 |
79
|
nnrpd |
|
120 |
119
|
adantr |
|
121 |
|
nnrp |
|
122 |
85 121
|
syl |
|
123 |
120 122
|
lerecd |
|
124 |
118 123
|
mpbid |
|
125 |
124
|
adantr |
|
126 |
111
|
adantr |
|
127 |
36 67
|
sseldi |
|
128 |
127
|
adantr |
|
129 |
78
|
simprd |
|
130 |
129
|
adantr |
|
131 |
63
|
adantr |
|
132 |
60
|
adantr |
|
133 |
|
id |
|
134 |
|
ovexd |
|
135 |
55
|
elrnmpt1 |
|
136 |
133 134 135
|
syl2anc |
|
137 |
136
|
adantl |
|
138 |
|
infrefilb |
|
139 |
131 132 137 138
|
syl3anc |
|
140 |
10 139
|
eqbrtrid |
|
141 |
126 128 41 130 140
|
ltletrd |
|
142 |
141
|
adantlr |
|
143 |
110 112 113 125 142
|
lelttrd |
|
144 |
85 25
|
syldanl |
|
145 |
144 110 106
|
ltaddsub2d |
|
146 |
143 145
|
mpbird |
|
147 |
109 146
|
eqbrtrd |
|
148 |
147
|
iftrued |
|
149 |
108 148
|
eqtrd |
|
150 |
149
|
prodeq2dv |
|
151 |
98 104 150
|
3eqtrd |
|
152 |
|
fvexd |
|
153 |
8
|
fvmpt2 |
|
154 |
85 152 153
|
syl2anc |
|
155 |
|
prodex |
|
156 |
155
|
a1i |
|
157 |
9
|
fvmpt2 |
|
158 |
85 156 157
|
syl2anc |
|
159 |
151 154 158
|
3eqtr4rd |
|
160 |
12 49 52 76 159
|
climeq |
|
161 |
45 160
|
mpbid |
|