Step |
Hyp |
Ref |
Expression |
1 |
|
simplr |
|
2 |
|
simpr1 |
|
3 |
|
simpr2 |
|
4 |
|
eqid |
|
5 |
|
eqid |
|
6 |
4 5
|
ressval2 |
|
7 |
1 2 3 6
|
syl3anc |
|
8 |
|
inass |
|
9 |
|
in12 |
|
10 |
8 9
|
eqtri |
|
11 |
4 5
|
ressbas |
|
12 |
3 11
|
syl |
|
13 |
12
|
ineq2d |
|
14 |
10 13
|
syl5req |
|
15 |
14
|
opeq2d |
|
16 |
7 15
|
oveq12d |
|
17 |
|
fvex |
|
18 |
17
|
inex2 |
|
19 |
|
setsabs |
|
20 |
2 18 19
|
sylancl |
|
21 |
16 20
|
eqtrd |
|
22 |
|
simpll |
|
23 |
|
ovexd |
|
24 |
|
simpr3 |
|
25 |
|
eqid |
|
26 |
|
eqid |
|
27 |
25 26
|
ressval2 |
|
28 |
22 23 24 27
|
syl3anc |
|
29 |
|
inss1 |
|
30 |
|
sstr |
|
31 |
29 30
|
mpan2 |
|
32 |
1 31
|
nsyl |
|
33 |
|
inex1g |
|
34 |
3 33
|
syl |
|
35 |
|
eqid |
|
36 |
35 5
|
ressval2 |
|
37 |
32 2 34 36
|
syl3anc |
|
38 |
21 28 37
|
3eqtr4d |
|
39 |
38
|
exp31 |
|
40 |
|
ovex |
|
41 |
25 26
|
ressid2 |
|
42 |
40 41
|
mp3an2 |
|
43 |
42
|
3ad2antr3 |
|
44 |
|
in32 |
|
45 |
|
simpr2 |
|
46 |
45 11
|
syl |
|
47 |
|
simpl |
|
48 |
46 47
|
eqsstrd |
|
49 |
|
df-ss |
|
50 |
48 49
|
sylib |
|
51 |
44 50
|
syl5req |
|
52 |
51
|
oveq2d |
|
53 |
5
|
ressinbas |
|
54 |
45 53
|
syl |
|
55 |
5
|
ressinbas |
|
56 |
45 33 55
|
3syl |
|
57 |
52 54 56
|
3eqtr4d |
|
58 |
43 57
|
eqtrd |
|
59 |
58
|
ex |
|
60 |
4 5
|
ressid2 |
|
61 |
60
|
3adant3r3 |
|
62 |
61
|
oveq1d |
|
63 |
|
inss2 |
|
64 |
|
simpl |
|
65 |
63 64
|
sstrid |
|
66 |
|
sseqin2 |
|
67 |
65 66
|
sylib |
|
68 |
8 67
|
syl5req |
|
69 |
68
|
oveq2d |
|
70 |
|
simpr3 |
|
71 |
5
|
ressinbas |
|
72 |
70 71
|
syl |
|
73 |
|
simpr2 |
|
74 |
73 33 55
|
3syl |
|
75 |
69 72 74
|
3eqtr4d |
|
76 |
62 75
|
eqtrd |
|
77 |
76
|
ex |
|
78 |
39 59 77
|
pm2.61ii |
|
79 |
78
|
3expib |
|
80 |
|
ress0 |
|
81 |
|
reldmress |
|
82 |
81
|
ovprc1 |
|
83 |
82
|
oveq1d |
|
84 |
81
|
ovprc1 |
|
85 |
80 83 84
|
3eqtr4a |
|
86 |
85
|
a1d |
|
87 |
79 86
|
pm2.61i |
|