Step |
Hyp |
Ref |
Expression |
1 |
|
ovex |
|
2 |
|
elfi2 |
|
3 |
1 2
|
ax-mp |
|
4 |
|
eldifi |
|
5 |
4
|
adantl |
|
6 |
5
|
elin2d |
|
7 |
|
elfpw |
|
8 |
7
|
simplbi |
|
9 |
5 8
|
syl |
|
10 |
9
|
sseld |
|
11 |
|
elrest |
|
12 |
11
|
adantr |
|
13 |
10 12
|
sylibd |
|
14 |
13
|
ralrimiv |
|
15 |
|
ineq1 |
|
16 |
15
|
eqeq2d |
|
17 |
16
|
ac6sfi |
|
18 |
6 14 17
|
syl2anc |
|
19 |
|
eldifsni |
|
20 |
19
|
ad2antlr |
|
21 |
|
iinin1 |
|
22 |
20 21
|
syl |
|
23 |
|
fvex |
|
24 |
|
simpllr |
|
25 |
|
ffn |
|
26 |
25
|
adantl |
|
27 |
|
fniinfv |
|
28 |
26 27
|
syl |
|
29 |
|
simplll |
|
30 |
|
simpr |
|
31 |
6
|
adantr |
|
32 |
|
intrnfi |
|
33 |
29 30 20 31 32
|
syl13anc |
|
34 |
28 33
|
eqeltrd |
|
35 |
|
elrestr |
|
36 |
23 24 34 35
|
mp3an2i |
|
37 |
22 36
|
eqeltrd |
|
38 |
|
intiin |
|
39 |
|
iineq2 |
|
40 |
38 39
|
syl5eq |
|
41 |
40
|
eleq1d |
|
42 |
37 41
|
syl5ibrcom |
|
43 |
42
|
expimpd |
|
44 |
43
|
exlimdv |
|
45 |
18 44
|
mpd |
|
46 |
|
eleq1 |
|
47 |
45 46
|
syl5ibrcom |
|
48 |
47
|
rexlimdva |
|
49 |
3 48
|
syl5bi |
|
50 |
|
simpr |
|
51 |
|
elrest |
|
52 |
23 50 51
|
sylancr |
|
53 |
|
elfi2 |
|
54 |
53
|
adantr |
|
55 |
|
eldifsni |
|
56 |
55
|
adantl |
|
57 |
|
iinin1 |
|
58 |
56 57
|
syl |
|
59 |
38
|
ineq1i |
|
60 |
58 59
|
eqtr4di |
|
61 |
|
ovexd |
|
62 |
|
eldifi |
|
63 |
62
|
adantl |
|
64 |
|
elfpw |
|
65 |
64
|
simplbi |
|
66 |
63 65
|
syl |
|
67 |
|
elrestr |
|
68 |
67
|
3expa |
|
69 |
68
|
ralrimiva |
|
70 |
69
|
adantr |
|
71 |
|
ssralv |
|
72 |
66 70 71
|
sylc |
|
73 |
63
|
elin2d |
|
74 |
|
iinfi |
|
75 |
61 72 56 73 74
|
syl13anc |
|
76 |
60 75
|
eqeltrrd |
|
77 |
|
eleq1 |
|
78 |
76 77
|
syl5ibrcom |
|
79 |
|
ineq1 |
|
80 |
79
|
eqeq2d |
|
81 |
80
|
imbi1d |
|
82 |
78 81
|
syl5ibrcom |
|
83 |
82
|
rexlimdva |
|
84 |
54 83
|
sylbid |
|
85 |
84
|
rexlimdv |
|
86 |
52 85
|
sylbid |
|
87 |
49 86
|
impbid |
|
88 |
87
|
eqrdv |
|
89 |
|
fi0 |
|
90 |
|
relxp |
|
91 |
|
restfn |
|
92 |
91
|
fndmi |
|
93 |
92
|
releqi |
|
94 |
90 93
|
mpbir |
|
95 |
94
|
ovprc |
|
96 |
95
|
fveq2d |
|
97 |
|
ianor |
|
98 |
|
fvprc |
|
99 |
98
|
oveq1d |
|
100 |
|
0rest |
|
101 |
99 100
|
eqtrdi |
|
102 |
94
|
ovprc2 |
|
103 |
101 102
|
jaoi |
|
104 |
97 103
|
sylbi |
|
105 |
89 96 104
|
3eqtr4a |
|
106 |
88 105
|
pm2.61i |
|