Step |
Hyp |
Ref |
Expression |
1 |
|
clwwlknonex2.v |
|
2 |
|
clwwlknonex2.e |
|
3 |
|
uz3m2nn |
|
4 |
3
|
nnne0d |
|
5 |
4
|
3ad2ant3 |
|
6 |
1 2
|
clwwlknonel |
|
7 |
5 6
|
syl |
|
8 |
|
simpr11 |
|
9 |
8
|
adantr |
|
10 |
|
simpll1 |
|
11 |
|
simpll2 |
|
12 |
|
ccatw2s1cl |
|
13 |
9 10 11 12
|
syl3anc |
|
14 |
1 2
|
clwwlknonex2lem2 |
|
15 |
|
simp11 |
|
16 |
15
|
ad2antlr |
|
17 |
|
ccatw2s1len |
|
18 |
16 17
|
syl |
|
19 |
18
|
oveq1d |
|
20 |
19
|
oveq2d |
|
21 |
|
simp3 |
|
22 |
|
simp2 |
|
23 |
21 22
|
anim12i |
|
24 |
23
|
adantr |
|
25 |
|
clwwlknonex2lem1 |
|
26 |
24 25
|
syl |
|
27 |
20 26
|
eqtrd |
|
28 |
14 27
|
raleqtrrdv |
|
29 |
|
ccatws1cl |
|
30 |
|
lswccats1 |
|
31 |
29 30
|
stoic3 |
|
32 |
16 10 11 31
|
syl3anc |
|
33 |
3
|
nngt0d |
|
34 |
|
breq2 |
|
35 |
33 34
|
imbitrrid |
|
36 |
35
|
3ad2ant2 |
|
37 |
36
|
com12 |
|
38 |
37
|
3ad2ant3 |
|
39 |
38
|
imp |
|
40 |
39
|
adantr |
|
41 |
|
ccat2s1fst |
|
42 |
16 40 41
|
syl2anc |
|
43 |
32 42
|
preq12d |
|
44 |
|
prcom |
|
45 |
44
|
eleq1i |
|
46 |
45
|
biimpi |
|
47 |
46
|
adantl |
|
48 |
|
preq2 |
|
49 |
48
|
eleq1d |
|
50 |
49
|
3ad2ant3 |
|
51 |
50
|
ad2antlr |
|
52 |
47 51
|
mpbird |
|
53 |
43 52
|
eqeltrd |
|
54 |
13 28 53
|
3jca |
|
55 |
17
|
3ad2ant1 |
|
56 |
55
|
3ad2ant1 |
|
57 |
56
|
ad2antlr |
|
58 |
|
oveq1 |
|
59 |
|
eluzelcn |
|
60 |
|
2cn |
|
61 |
|
npcan |
|
62 |
59 60 61
|
sylancl |
|
63 |
58 62
|
sylan9eq |
|
64 |
63
|
ex |
|
65 |
64
|
3ad2ant2 |
|
66 |
65
|
com12 |
|
67 |
66
|
3ad2ant3 |
|
68 |
67
|
imp |
|
69 |
68
|
adantr |
|
70 |
57 69
|
eqtrd |
|
71 |
54 70
|
jca |
|
72 |
71
|
exp31 |
|
73 |
7 72
|
sylbid |
|
74 |
73
|
com23 |
|
75 |
74
|
3imp |
|
76 |
|
eluzge3nn |
|
77 |
1 2
|
isclwwlknx |
|
78 |
76 77
|
syl |
|
79 |
78
|
3ad2ant3 |
|
80 |
79
|
3ad2ant1 |
|
81 |
75 80
|
mpbird |
|