Step |
Hyp |
Ref |
Expression |
1 |
|
hlhilset.h |
|
2 |
|
hlhilset.l |
|
3 |
|
hlhilset.u |
|
4 |
|
hlhilset.v |
|
5 |
|
hlhilset.p |
|
6 |
|
hlhilset.e |
|
7 |
|
hlhilset.g |
|
8 |
|
hlhilset.r |
|
9 |
|
hlhilset.t |
|
10 |
|
hlhilset.s |
|
11 |
|
hlhilset.i |
|
12 |
|
hlhilset.k |
|
13 |
|
elex |
|
14 |
13
|
adantr |
|
15 |
12 14
|
syl |
|
16 |
1
|
fvexi |
|
17 |
16
|
mptex |
|
18 |
|
nfcv |
|
19 |
|
nfcv |
|
20 |
|
nfcsb1v |
|
21 |
19 20
|
nfmpt |
|
22 |
|
fveq2 |
|
23 |
22 1
|
eqtr4di |
|
24 |
|
csbeq1a |
|
25 |
23 24
|
mpteq12dv |
|
26 |
|
df-hlhil |
|
27 |
18 21 25 26
|
fvmptf |
|
28 |
15 17 27
|
sylancl |
|
29 |
15
|
adantr |
|
30 |
|
fvexd |
|
31 |
|
fvexd |
|
32 |
|
id |
|
33 |
|
id |
|
34 |
|
simpr |
|
35 |
34
|
fveq2d |
|
36 |
|
simplr |
|
37 |
35 36
|
fveq12d |
|
38 |
37 3
|
eqtr4di |
|
39 |
33 38
|
sylan9eqr |
|
40 |
39
|
fveq2d |
|
41 |
40 4
|
eqtr4di |
|
42 |
32 41
|
sylan9eqr |
|
43 |
42
|
opeq2d |
|
44 |
39
|
adantr |
|
45 |
44
|
fveq2d |
|
46 |
45 5
|
eqtr4di |
|
47 |
46
|
opeq2d |
|
48 |
34
|
fveq2d |
|
49 |
48 36
|
fveq12d |
|
50 |
49 6
|
eqtr4di |
|
51 |
34
|
fveq2d |
|
52 |
51 36
|
fveq12d |
|
53 |
52 7
|
eqtr4di |
|
54 |
53
|
opeq2d |
|
55 |
50 54
|
oveq12d |
|
56 |
55 8
|
eqtr4di |
|
57 |
56
|
opeq2d |
|
58 |
57
|
ad2antrr |
|
59 |
43 47 58
|
tpeq123d |
|
60 |
44
|
fveq2d |
|
61 |
60 9
|
eqtr4di |
|
62 |
61
|
opeq2d |
|
63 |
34
|
fveq2d |
|
64 |
63 36
|
fveq12d |
|
65 |
64 10
|
eqtr4di |
|
66 |
65
|
ad2antrr |
|
67 |
66
|
fveq1d |
|
68 |
67
|
fveq1d |
|
69 |
42 42 68
|
mpoeq123dv |
|
70 |
69 11
|
eqtr4di |
|
71 |
70
|
opeq2d |
|
72 |
62 71
|
preq12d |
|
73 |
59 72
|
uneq12d |
|
74 |
31 73
|
csbied |
|
75 |
30 74
|
csbied |
|
76 |
29 75
|
csbied |
|
77 |
12
|
simprd |
|
78 |
|
tpex |
|
79 |
|
prex |
|
80 |
78 79
|
unex |
|
81 |
80
|
a1i |
|
82 |
28 76 77 81
|
fvmptd |
|
83 |
2 82
|
syl5eq |
|