Step |
Hyp |
Ref |
Expression |
1 |
|
supxrgere.xph |
|
2 |
|
supxrgere.a |
|
3 |
|
supxrgere.b |
|
4 |
|
supxrgere.y |
|
5 |
|
rexr |
|
6 |
|
pnfxr |
|
7 |
6
|
a1i |
|
8 |
|
ltpnf |
|
9 |
5 7 8
|
xrltled |
|
10 |
3 9
|
syl |
|
11 |
10
|
adantr |
|
12 |
|
id |
|
13 |
12
|
eqcomd |
|
14 |
13
|
adantl |
|
15 |
11 14
|
breqtrd |
|
16 |
|
simpl |
|
17 |
|
1rp |
|
18 |
|
nfcv |
|
19 |
|
nfv |
|
20 |
1 19
|
nfan |
|
21 |
|
nfv |
|
22 |
20 21
|
nfim |
|
23 |
|
eleq1 |
|
24 |
23
|
anbi2d |
|
25 |
|
oveq2 |
|
26 |
25
|
breq1d |
|
27 |
26
|
rexbidv |
|
28 |
24 27
|
imbi12d |
|
29 |
18 22 28 4
|
vtoclgf |
|
30 |
17 29
|
ax-mp |
|
31 |
17 30
|
mpan2 |
|
32 |
31
|
adantr |
|
33 |
|
mnfxr |
|
34 |
33
|
a1i |
|
35 |
2
|
sselda |
|
36 |
35
|
3adant3 |
|
37 |
|
supxrcl |
|
38 |
2 37
|
syl |
|
39 |
38
|
3ad2ant1 |
|
40 |
|
peano2rem |
|
41 |
3 40
|
syl |
|
42 |
41
|
rexrd |
|
43 |
42
|
adantr |
|
44 |
43
|
3ad2antl1 |
|
45 |
36
|
adantr |
|
46 |
33
|
a1i |
|
47 |
|
simpl3 |
|
48 |
|
simpr |
|
49 |
35
|
adantr |
|
50 |
33
|
a1i |
|
51 |
|
xrlenlt |
|
52 |
49 50 51
|
syl2anc |
|
53 |
48 52
|
mpbird |
|
54 |
53
|
3adantl3 |
|
55 |
44 45 46 47 54
|
xrltletrd |
|
56 |
|
nltmnf |
|
57 |
42 56
|
syl |
|
58 |
57
|
adantr |
|
59 |
58
|
3ad2antl1 |
|
60 |
55 59
|
condan |
|
61 |
2
|
adantr |
|
62 |
|
simpr |
|
63 |
|
supxrub |
|
64 |
61 62 63
|
syl2anc |
|
65 |
64
|
3adant3 |
|
66 |
34 36 39 60 65
|
xrltletrd |
|
67 |
66
|
3exp |
|
68 |
67
|
adantr |
|
69 |
68
|
rexlimdv |
|
70 |
32 69
|
mpd |
|
71 |
|
simpr |
|
72 |
|
nltpnft |
|
73 |
38 72
|
syl |
|
74 |
73
|
adantr |
|
75 |
71 74
|
mtbid |
|
76 |
75
|
notnotrd |
|
77 |
70 76
|
jca |
|
78 |
38
|
adantr |
|
79 |
|
xrrebnd |
|
80 |
78 79
|
syl |
|
81 |
77 80
|
mpbird |
|
82 |
|
simpl |
|
83 |
|
simpr |
|
84 |
82
|
simprd |
|
85 |
3
|
ad2antrr |
|
86 |
84 85
|
ltnled |
|
87 |
83 86
|
mpbird |
|
88 |
|
simpll |
|
89 |
3
|
adantr |
|
90 |
|
simpr |
|
91 |
89 90
|
resubcld |
|
92 |
91
|
adantr |
|
93 |
|
simpr |
|
94 |
90
|
adantr |
|
95 |
88 3
|
syl |
|
96 |
94 95
|
posdifd |
|
97 |
93 96
|
mpbid |
|
98 |
92 97
|
elrpd |
|
99 |
|
ovex |
|
100 |
|
nfcv |
|
101 |
|
nfv |
|
102 |
1 101
|
nfan |
|
103 |
|
nfv |
|
104 |
102 103
|
nfim |
|
105 |
|
eleq1 |
|
106 |
105
|
anbi2d |
|
107 |
|
oveq2 |
|
108 |
107
|
breq1d |
|
109 |
108
|
rexbidv |
|
110 |
106 109
|
imbi12d |
|
111 |
100 104 110 4
|
vtoclgf |
|
112 |
99 111
|
ax-mp |
|
113 |
88 98 112
|
syl2anc |
|
114 |
3
|
recnd |
|
115 |
114
|
ad3antrrr |
|
116 |
90
|
recnd |
|
117 |
116
|
ad2antrr |
|
118 |
115 117
|
nncand |
|
119 |
118
|
eqcomd |
|
120 |
|
simpr |
|
121 |
119 120
|
eqbrtrd |
|
122 |
121
|
ex |
|
123 |
122
|
adantr |
|
124 |
123
|
reximdva |
|
125 |
113 124
|
mpd |
|
126 |
82 87 125
|
syl2anc |
|
127 |
61 37
|
syl |
|
128 |
35 127
|
xrlenltd |
|
129 |
64 128
|
mpbid |
|
130 |
129
|
ralrimiva |
|
131 |
|
ralnex |
|
132 |
130 131
|
sylib |
|
133 |
132
|
ad2antrr |
|
134 |
126 133
|
condan |
|
135 |
16 81 134
|
syl2anc |
|
136 |
15 135
|
pm2.61dan |
|