Step |
Hyp |
Ref |
Expression |
1 |
|
rngcrescrhm.u |
|
2 |
|
rngcrescrhm.c |
|
3 |
|
rngcrescrhm.r |
|
4 |
|
rngcrescrhm.h |
|
5 |
|
simpl |
|
6 |
5
|
adantr |
|
7 |
|
simpr |
|
8 |
7
|
adantr |
|
9 |
|
simpl |
|
10 |
9
|
adantl |
|
11 |
1 2 3 4
|
rhmsubclem2 |
|
12 |
6 8 10 11
|
syl3anc |
|
13 |
12
|
eleq2d |
|
14 |
|
simpr |
|
15 |
14
|
adantl |
|
16 |
1 2 3 4
|
rhmsubclem2 |
|
17 |
6 10 15 16
|
syl3anc |
|
18 |
17
|
eleq2d |
|
19 |
13 18
|
anbi12d |
|
20 |
|
rhmco |
|
21 |
20
|
ancoms |
|
22 |
19 21
|
syl6bi |
|
23 |
22
|
imp |
|
24 |
1
|
ad3antrrr |
|
25 |
2
|
eqcomi |
|
26 |
25
|
fveq2i |
|
27 |
|
inss2 |
|
28 |
3 27
|
eqsstrdi |
|
29 |
28
|
sselda |
|
30 |
29
|
adantr |
|
31 |
30
|
adantr |
|
32 |
28
|
sseld |
|
33 |
32
|
adantrd |
|
34 |
33
|
adantr |
|
35 |
34
|
imp |
|
36 |
35
|
adantr |
|
37 |
28
|
sseld |
|
38 |
37
|
adantld |
|
39 |
38
|
adantr |
|
40 |
39
|
imp |
|
41 |
40
|
adantr |
|
42 |
4
|
oveqi |
|
43 |
8 10
|
ovresd |
|
44 |
42 43
|
syl5eq |
|
45 |
44
|
eleq2d |
|
46 |
|
eqid |
|
47 |
|
eqid |
|
48 |
46 47
|
rhmf |
|
49 |
45 48
|
syl6bi |
|
50 |
49
|
com12 |
|
51 |
50
|
adantr |
|
52 |
51
|
impcom |
|
53 |
4
|
oveqi |
|
54 |
|
ovres |
|
55 |
54
|
adantl |
|
56 |
53 55
|
syl5eq |
|
57 |
56
|
eleq2d |
|
58 |
|
eqid |
|
59 |
47 58
|
rhmf |
|
60 |
57 59
|
syl6bi |
|
61 |
60
|
com12 |
|
62 |
61
|
adantl |
|
63 |
62
|
impcom |
|
64 |
2 24 26 31 36 41 52 63
|
rngcco |
|
65 |
1 2 3 4
|
rhmsubclem2 |
|
66 |
6 8 15 65
|
syl3anc |
|
67 |
66
|
adantr |
|
68 |
23 64 67
|
3eltr4d |
|