Step |
Hyp |
Ref |
Expression |
1 |
|
ioorrnopnxrlem.x |
|
2 |
|
ioorrnopnxrlem.a |
|
3 |
|
ioorrnopnxrlem.b |
|
4 |
|
ioorrnopnxrlem.f |
|
5 |
|
ioorrnopnxrlem.l |
|
6 |
|
ioorrnopnxrlem.r |
|
7 |
|
ioorrnopnxrlem.v |
|
8 |
7
|
a1i |
|
9 |
|
iftrue |
|
10 |
9
|
adantl |
|
11 |
4
|
adantr |
|
12 |
|
simpr |
|
13 |
|
fvixp2 |
|
14 |
11 12 13
|
syl2anc |
|
15 |
14
|
elioored |
|
16 |
|
1red |
|
17 |
15 16
|
resubcld |
|
18 |
17
|
adantr |
|
19 |
10 18
|
eqeltrd |
|
20 |
|
iffalse |
|
21 |
20
|
adantl |
|
22 |
|
neqne |
|
23 |
22
|
adantl |
|
24 |
2
|
ffvelrnda |
|
25 |
24
|
adantr |
|
26 |
|
simpr |
|
27 |
|
pnfxr |
|
28 |
27
|
a1i |
|
29 |
15
|
rexrd |
|
30 |
3
|
ffvelrnda |
|
31 |
|
ioogtlb |
|
32 |
24 30 14 31
|
syl3anc |
|
33 |
15
|
ltpnfd |
|
34 |
24 29 28 32 33
|
xrlttrd |
|
35 |
24 28 34
|
xrltned |
|
36 |
35
|
adantr |
|
37 |
25 26 36
|
xrred |
|
38 |
23 37
|
syldan |
|
39 |
21 38
|
eqeltrd |
|
40 |
19 39
|
pm2.61dan |
|
41 |
40 5
|
fmptd |
|
42 |
|
iftrue |
|
43 |
42
|
adantl |
|
44 |
15 16
|
readdcld |
|
45 |
44
|
adantr |
|
46 |
43 45
|
eqeltrd |
|
47 |
|
iffalse |
|
48 |
47
|
adantl |
|
49 |
|
neqne |
|
50 |
49
|
adantl |
|
51 |
30
|
adantr |
|
52 |
|
mnfxr |
|
53 |
52
|
a1i |
|
54 |
15
|
mnfltd |
|
55 |
|
iooltub |
|
56 |
24 30 14 55
|
syl3anc |
|
57 |
53 29 30 54 56
|
xrlttrd |
|
58 |
53 30 57
|
xrgtned |
|
59 |
58
|
adantr |
|
60 |
|
simpr |
|
61 |
51 59 60
|
xrred |
|
62 |
50 61
|
syldan |
|
63 |
48 62
|
eqeltrd |
|
64 |
46 63
|
pm2.61dan |
|
65 |
64 6
|
fmptd |
|
66 |
1 41 65
|
ioorrnopn |
|
67 |
8 66
|
eqeltrd |
|
68 |
4
|
elexd |
|
69 |
|
ixpfn |
|
70 |
4 69
|
syl |
|
71 |
41
|
ffvelrnda |
|
72 |
71
|
rexrd |
|
73 |
65
|
ffvelrnda |
|
74 |
73
|
rexrd |
|
75 |
5
|
a1i |
|
76 |
40
|
elexd |
|
77 |
75 76
|
fvmpt2d |
|
78 |
77
|
adantr |
|
79 |
78 10
|
eqtrd |
|
80 |
15
|
ltm1d |
|
81 |
80
|
adantr |
|
82 |
79 81
|
eqbrtrd |
|
83 |
77
|
adantr |
|
84 |
83 21
|
eqtrd |
|
85 |
32
|
adantr |
|
86 |
84 85
|
eqbrtrd |
|
87 |
82 86
|
pm2.61dan |
|
88 |
15
|
ltp1d |
|
89 |
88
|
adantr |
|
90 |
6
|
a1i |
|
91 |
64
|
elexd |
|
92 |
90 91
|
fvmpt2d |
|
93 |
92
|
adantr |
|
94 |
93 43
|
eqtrd |
|
95 |
94
|
eqcomd |
|
96 |
89 95
|
breqtrd |
|
97 |
56
|
adantr |
|
98 |
92
|
adantr |
|
99 |
98 48
|
eqtrd |
|
100 |
99
|
eqcomd |
|
101 |
97 100
|
breqtrd |
|
102 |
96 101
|
pm2.61dan |
|
103 |
72 74 15 87 102
|
eliood |
|
104 |
103
|
ralrimiva |
|
105 |
68 70 104
|
3jca |
|
106 |
|
elixp2 |
|
107 |
105 106
|
sylibr |
|
108 |
107 7
|
eleqtrrdi |
|
109 |
24
|
adantr |
|
110 |
72
|
adantr |
|
111 |
19
|
mnfltd |
|
112 |
111 10
|
breqtrd |
|
113 |
|
simpr |
|
114 |
113 79
|
breq12d |
|
115 |
112 114
|
mpbird |
|
116 |
109 110 115
|
xrltled |
|
117 |
84
|
eqcomd |
|
118 |
38 117
|
eqled |
|
119 |
116 118
|
pm2.61dan |
|
120 |
74
|
adantr |
|
121 |
30
|
adantr |
|
122 |
45
|
ltpnfd |
|
123 |
|
simpr |
|
124 |
94 123
|
breq12d |
|
125 |
122 124
|
mpbird |
|
126 |
120 121 125
|
xrltled |
|
127 |
73
|
adantr |
|
128 |
127 99
|
eqled |
|
129 |
126 128
|
pm2.61dan |
|
130 |
|
ioossioo |
|
131 |
24 30 119 129 130
|
syl22anc |
|
132 |
131
|
ralrimiva |
|
133 |
|
ss2ixp |
|
134 |
132 133
|
syl |
|
135 |
8 134
|
eqsstrd |
|
136 |
108 135
|
jca |
|
137 |
|
eleq2 |
|
138 |
|
sseq1 |
|
139 |
137 138
|
anbi12d |
|
140 |
139
|
rspcev |
|
141 |
67 136 140
|
syl2anc |
|