Step |
Hyp |
Ref |
Expression |
1 |
|
simp3 |
|
2 |
|
rexr |
|
3 |
2
|
3ad2ant2 |
|
4 |
|
iccssxr |
|
5 |
|
volf |
|
6 |
5
|
ffvelrni |
|
7 |
4 6
|
sseldi |
|
8 |
7
|
3ad2ant1 |
|
9 |
|
xrltnle |
|
10 |
3 8 9
|
syl2anc |
|
11 |
1 10
|
mpbid |
|
12 |
|
negeq |
|
13 |
|
id |
|
14 |
12 13
|
oveq12d |
|
15 |
14
|
ineq2d |
|
16 |
|
eqid |
|
17 |
|
ovex |
|
18 |
17
|
inex2 |
|
19 |
15 16 18
|
fvmpt |
|
20 |
19
|
iuneq2i |
|
21 |
|
iunin2 |
|
22 |
20 21
|
eqtri |
|
23 |
|
simpl1 |
|
24 |
|
nnre |
|
25 |
24
|
adantl |
|
26 |
25
|
renegcld |
|
27 |
|
iccmbl |
|
28 |
26 25 27
|
syl2anc |
|
29 |
|
inmbl |
|
30 |
23 28 29
|
syl2anc |
|
31 |
15
|
cbvmptv |
|
32 |
30 31
|
fmptd |
|
33 |
32
|
ffnd |
|
34 |
|
fniunfv |
|
35 |
33 34
|
syl |
|
36 |
|
mblss |
|
37 |
36
|
3ad2ant1 |
|
38 |
37
|
sselda |
|
39 |
|
recn |
|
40 |
39
|
abscld |
|
41 |
|
arch |
|
42 |
40 41
|
syl |
|
43 |
|
ltle |
|
44 |
40 24 43
|
syl2an |
|
45 |
|
id |
|
46 |
45
|
3expib |
|
47 |
46
|
adantr |
|
48 |
|
absle |
|
49 |
24 48
|
sylan2 |
|
50 |
24
|
adantl |
|
51 |
50
|
renegcld |
|
52 |
|
elicc2 |
|
53 |
51 50 52
|
syl2anc |
|
54 |
47 49 53
|
3imtr4d |
|
55 |
44 54
|
syld |
|
56 |
55
|
reximdva |
|
57 |
42 56
|
mpd |
|
58 |
38 57
|
syl |
|
59 |
58
|
ex |
|
60 |
|
eliun |
|
61 |
59 60
|
syl6ibr |
|
62 |
61
|
ssrdv |
|
63 |
|
df-ss |
|
64 |
62 63
|
sylib |
|
65 |
22 35 64
|
3eqtr3a |
|
66 |
65
|
fveq2d |
|
67 |
|
peano2re |
|
68 |
25 67
|
syl |
|
69 |
68
|
renegcld |
|
70 |
25
|
lep1d |
|
71 |
25 68
|
lenegd |
|
72 |
70 71
|
mpbid |
|
73 |
|
iccss |
|
74 |
69 68 72 70 73
|
syl22anc |
|
75 |
|
sslin |
|
76 |
74 75
|
syl |
|
77 |
19
|
adantl |
|
78 |
|
peano2nn |
|
79 |
78
|
adantl |
|
80 |
|
negeq |
|
81 |
|
id |
|
82 |
80 81
|
oveq12d |
|
83 |
82
|
ineq2d |
|
84 |
|
ovex |
|
85 |
84
|
inex2 |
|
86 |
83 16 85
|
fvmpt |
|
87 |
79 86
|
syl |
|
88 |
76 77 87
|
3sstr4d |
|
89 |
88
|
ralrimiva |
|
90 |
|
volsup |
|
91 |
32 89 90
|
syl2anc |
|
92 |
66 91
|
eqtr3d |
|
93 |
92
|
breq1d |
|
94 |
|
imassrn |
|
95 |
|
frn |
|
96 |
5 95
|
ax-mp |
|
97 |
96 4
|
sstri |
|
98 |
94 97
|
sstri |
|
99 |
|
supxrleub |
|
100 |
98 3 99
|
sylancr |
|
101 |
|
ffn |
|
102 |
5 101
|
ax-mp |
|
103 |
32
|
frnd |
|
104 |
|
breq1 |
|
105 |
104
|
ralima |
|
106 |
102 103 105
|
sylancr |
|
107 |
|
fveq2 |
|
108 |
107
|
breq1d |
|
109 |
108
|
ralrn |
|
110 |
33 109
|
syl |
|
111 |
19
|
fveq2d |
|
112 |
111
|
breq1d |
|
113 |
112
|
ralbiia |
|
114 |
110 113
|
bitrdi |
|
115 |
106 114
|
bitrd |
|
116 |
93 100 115
|
3bitrd |
|
117 |
11 116
|
mtbid |
|
118 |
|
rexnal |
|
119 |
117 118
|
sylibr |
|
120 |
3
|
adantr |
|
121 |
5
|
ffvelrni |
|
122 |
4 121
|
sseldi |
|
123 |
30 122
|
syl |
|
124 |
|
xrltnle |
|
125 |
120 123 124
|
syl2anc |
|
126 |
125
|
rexbidva |
|
127 |
119 126
|
mpbird |
|