Step |
Hyp |
Ref |
Expression |
1 |
|
rlimcnp2.a |
|
2 |
|
rlimcnp2.0 |
|
3 |
|
rlimcnp2.b |
|
4 |
|
rlimcnp2.c |
|
5 |
|
rlimcnp2.r |
|
6 |
|
rlimcnp2.d |
|
7 |
|
rlimcnp2.s |
|
8 |
|
rlimcnp2.j |
|
9 |
|
rlimcnp2.k |
|
10 |
|
inss1 |
|
11 |
|
resmpt |
|
12 |
10 11
|
mp1i |
|
13 |
|
0xr |
|
14 |
|
0lt1 |
|
15 |
|
df-ioo |
|
16 |
|
df-ico |
|
17 |
|
xrltletr |
|
18 |
15 16 17
|
ixxss1 |
|
19 |
13 14 18
|
mp2an |
|
20 |
|
ioorp |
|
21 |
19 20
|
sseqtri |
|
22 |
|
sslin |
|
23 |
21 22
|
ax-mp |
|
24 |
|
resmpt |
|
25 |
23 24
|
mp1i |
|
26 |
12 25
|
eqtr4d |
|
27 |
|
resres |
|
28 |
|
resres |
|
29 |
26 27 28
|
3eqtr4g |
|
30 |
5
|
fmpttd |
|
31 |
30
|
ffnd |
|
32 |
|
fnresdm |
|
33 |
31 32
|
syl |
|
34 |
33
|
reseq1d |
|
35 |
|
elinel1 |
|
36 |
35 5
|
sylan2 |
|
37 |
36
|
fmpttd |
|
38 |
|
frel |
|
39 |
37 38
|
syl |
|
40 |
|
eqid |
|
41 |
40 36
|
dmmptd |
|
42 |
|
inss1 |
|
43 |
41 42
|
eqsstrdi |
|
44 |
|
relssres |
|
45 |
39 43 44
|
syl2anc |
|
46 |
45
|
reseq1d |
|
47 |
29 34 46
|
3eqtr3d |
|
48 |
47
|
breq1d |
|
49 |
|
1red |
|
50 |
30 3 49
|
rlimresb |
|
51 |
42 3
|
sstrid |
|
52 |
37 51 49
|
rlimresb |
|
53 |
48 50 52
|
3bitr4d |
|
54 |
|
inss2 |
|
55 |
54
|
a1i |
|
56 |
55
|
sselda |
|
57 |
56
|
rpreccld |
|
58 |
57
|
rpne0d |
|
59 |
58
|
neneqd |
|
60 |
59
|
iffalsed |
|
61 |
|
oveq2 |
|
62 |
|
rpcnne0 |
|
63 |
|
recrec |
|
64 |
56 62 63
|
3syl |
|
65 |
61 64
|
sylan9eqr |
|
66 |
65
|
eqcomd |
|
67 |
66 7
|
syl |
|
68 |
67
|
eqcomd |
|
69 |
57 68
|
csbied |
|
70 |
60 69
|
eqtrd |
|
71 |
70
|
mpteq2dva |
|
72 |
71
|
breq1d |
|
73 |
4
|
ad2antrr |
|
74 |
1
|
sselda |
|
75 |
|
0re |
|
76 |
|
pnfxr |
|
77 |
|
elico2 |
|
78 |
75 76 77
|
mp2an |
|
79 |
74 78
|
sylib |
|
80 |
79
|
simp1d |
|
81 |
80
|
adantr |
|
82 |
79
|
simp2d |
|
83 |
|
leloe |
|
84 |
75 80 83
|
sylancr |
|
85 |
82 84
|
mpbid |
|
86 |
85
|
ord |
|
87 |
|
eqcom |
|
88 |
86 87
|
syl6ib |
|
89 |
88
|
con1d |
|
90 |
89
|
imp |
|
91 |
81 90
|
elrpd |
|
92 |
|
rpcnne0 |
|
93 |
|
recrec |
|
94 |
92 93
|
syl |
|
95 |
91 94
|
syl |
|
96 |
95
|
csbeq1d |
|
97 |
|
oveq2 |
|
98 |
97
|
csbeq1d |
|
99 |
98
|
eleq1d |
|
100 |
69 36
|
eqeltrd |
|
101 |
100
|
ralrimiva |
|
102 |
101
|
ad2antrr |
|
103 |
|
simplr |
|
104 |
|
simpll |
|
105 |
|
eleq1 |
|
106 |
97
|
eleq1d |
|
107 |
105 106
|
bibi12d |
|
108 |
6
|
ralrimiva |
|
109 |
108
|
adantr |
|
110 |
|
rpreccl |
|
111 |
110
|
adantl |
|
112 |
107 109 111
|
rspcdva |
|
113 |
94
|
adantl |
|
114 |
113
|
eleq1d |
|
115 |
112 114
|
bitr2d |
|
116 |
104 91 115
|
syl2anc |
|
117 |
103 116
|
mpbid |
|
118 |
91
|
rpreccld |
|
119 |
117 118
|
elind |
|
120 |
99 102 119
|
rspcdva |
|
121 |
96 120
|
eqeltrrd |
|
122 |
73 121
|
ifclda |
|
123 |
111
|
biantrud |
|
124 |
115 123
|
bitrd |
|
125 |
|
elin |
|
126 |
124 125
|
syl6bbr |
|
127 |
|
iftrue |
|
128 |
|
eqeq1 |
|
129 |
|
csbeq1 |
|
130 |
128 129
|
ifbieq2d |
|
131 |
1 2 55 122 126 127 130 8 9
|
rlimcnp |
|
132 |
|
nfcv |
|
133 |
|
nfv |
|
134 |
|
nfcv |
|
135 |
|
nfcsb1v |
|
136 |
133 134 135
|
nfif |
|
137 |
|
eqeq1 |
|
138 |
|
csbeq1a |
|
139 |
137 138
|
ifbieq2d |
|
140 |
132 136 139
|
cbvmpt |
|
141 |
140
|
eleq1i |
|
142 |
131 141
|
syl6bbr |
|
143 |
53 72 142
|
3bitr2d |
|