Step |
Hyp |
Ref |
Expression |
1 |
|
ptrecube.r |
|
2 |
|
ptrecube.d |
|
3 |
|
fzfi |
|
4 |
|
retop |
|
5 |
|
fnconstg |
|
6 |
4 5
|
ax-mp |
|
7 |
|
eqid |
|
8 |
7
|
ptval |
|
9 |
3 6 8
|
mp2an |
|
10 |
1 9
|
eqtri |
|
11 |
10
|
eleq2i |
|
12 |
|
tg2 |
|
13 |
7
|
elpt |
|
14 |
|
fvex |
|
15 |
14
|
fvconst2 |
|
16 |
15
|
eleq2d |
|
17 |
16
|
ralbiia |
|
18 |
|
elixp2 |
|
19 |
18
|
simp3bi |
|
20 |
|
r19.26 |
|
21 |
|
uniretop |
|
22 |
21
|
eltopss |
|
23 |
4 22
|
mpan |
|
24 |
23
|
sselda |
|
25 |
2
|
rexmet |
|
26 |
|
eqid |
|
27 |
2 26
|
tgioo |
|
28 |
27
|
mopni2 |
|
29 |
25 28
|
mp3an1 |
|
30 |
|
r19.42v |
|
31 |
24 29 30
|
sylanbrc |
|
32 |
31
|
ralimi |
|
33 |
|
oveq2 |
|
34 |
33
|
sseq1d |
|
35 |
34
|
anbi2d |
|
36 |
35
|
ac6sfi |
|
37 |
3 32 36
|
sylancr |
|
38 |
|
1rp |
|
39 |
38
|
a1i |
|
40 |
|
frn |
|
41 |
40
|
adantr |
|
42 |
|
ffn |
|
43 |
|
fnfi |
|
44 |
42 3 43
|
sylancl |
|
45 |
|
rnfi |
|
46 |
44 45
|
syl |
|
47 |
46
|
adantr |
|
48 |
|
dm0rn0 |
|
49 |
|
fdm |
|
50 |
49
|
eqeq1d |
|
51 |
48 50
|
bitr3id |
|
52 |
51
|
necon3abid |
|
53 |
52
|
biimpar |
|
54 |
|
rpssre |
|
55 |
40 54
|
sstrdi |
|
56 |
55
|
adantr |
|
57 |
|
ltso |
|
58 |
|
fiinfcl |
|
59 |
57 58
|
mpan |
|
60 |
47 53 56 59
|
syl3anc |
|
61 |
41 60
|
sseldd |
|
62 |
39 61
|
ifclda |
|
63 |
62
|
adantr |
|
64 |
62
|
adantr |
|
65 |
64
|
rpxrd |
|
66 |
|
ffvelrn |
|
67 |
66
|
rpxrd |
|
68 |
|
ne0i |
|
69 |
|
ifnefalse |
|
70 |
68 69
|
syl |
|
71 |
70
|
adantl |
|
72 |
55
|
adantr |
|
73 |
|
0re |
|
74 |
|
rpge0 |
|
75 |
74
|
rgen |
|
76 |
|
ssralv |
|
77 |
40 75 76
|
mpisyl |
|
78 |
|
breq1 |
|
79 |
78
|
ralbidv |
|
80 |
79
|
rspcev |
|
81 |
73 77 80
|
sylancr |
|
82 |
81
|
adantr |
|
83 |
|
fnfvelrn |
|
84 |
42 83
|
sylan |
|
85 |
|
infrelb |
|
86 |
72 82 84 85
|
syl3anc |
|
87 |
71 86
|
eqbrtrd |
|
88 |
65 67 87
|
jca31 |
|
89 |
|
ssbl |
|
90 |
89
|
3expb |
|
91 |
25 90
|
mpanl1 |
|
92 |
91
|
ancoms |
|
93 |
88 92
|
sylan |
|
94 |
|
sstr2 |
|
95 |
93 94
|
syl |
|
96 |
95
|
expimpd |
|
97 |
96
|
ralimdva |
|
98 |
97
|
imp |
|
99 |
2
|
fveq2i |
|
100 |
99
|
oveqi |
|
101 |
100
|
sseq1i |
|
102 |
101
|
ralbii |
|
103 |
|
nfv |
|
104 |
102 103
|
nfxfr |
|
105 |
|
oveq2 |
|
106 |
105
|
sseq1d |
|
107 |
106
|
ralbidv |
|
108 |
104 107
|
rspce |
|
109 |
63 98 108
|
syl2anc |
|
110 |
109
|
exlimiv |
|
111 |
37 110
|
syl |
|
112 |
20 111
|
sylbir |
|
113 |
19 112
|
sylan2 |
|
114 |
17 113
|
sylanb |
|
115 |
|
sstr2 |
|
116 |
|
ss2ixp |
|
117 |
115 116
|
syl11 |
|
118 |
117
|
reximdv |
|
119 |
114 118
|
syl5com |
|
120 |
119
|
expimpd |
|
121 |
|
eleq2 |
|
122 |
|
sseq1 |
|
123 |
121 122
|
anbi12d |
|
124 |
123
|
imbi1d |
|
125 |
120 124
|
syl5ibrcom |
|
126 |
125
|
3ad2ant2 |
|
127 |
126
|
imp |
|
128 |
127
|
exlimiv |
|
129 |
13 128
|
sylbi |
|
130 |
129
|
rexlimiv |
|
131 |
12 130
|
syl |
|
132 |
11 131
|
sylanb |
|