Step |
Hyp |
Ref |
Expression |
1 |
|
nnmordi |
|
2 |
1
|
ex |
|
3 |
2
|
impcomd |
|
4 |
3
|
3adant1 |
|
5 |
|
ne0i |
|
6 |
|
nnm0r |
|
7 |
|
oveq1 |
|
8 |
7
|
eqeq1d |
|
9 |
6 8
|
syl5ibrcom |
|
10 |
9
|
necon3d |
|
11 |
5 10
|
syl5 |
|
12 |
11
|
adantr |
|
13 |
|
nnord |
|
14 |
|
ord0eln0 |
|
15 |
13 14
|
syl |
|
16 |
15
|
adantl |
|
17 |
12 16
|
sylibrd |
|
18 |
17
|
3adant1 |
|
19 |
|
oveq2 |
|
20 |
19
|
a1i |
|
21 |
|
nnmordi |
|
22 |
21
|
3adantl2 |
|
23 |
20 22
|
orim12d |
|
24 |
23
|
con3d |
|
25 |
|
simpl3 |
|
26 |
|
simpl1 |
|
27 |
|
nnmcl |
|
28 |
25 26 27
|
syl2anc |
|
29 |
|
simpl2 |
|
30 |
|
nnmcl |
|
31 |
25 29 30
|
syl2anc |
|
32 |
|
nnord |
|
33 |
|
nnord |
|
34 |
|
ordtri2 |
|
35 |
32 33 34
|
syl2an |
|
36 |
28 31 35
|
syl2anc |
|
37 |
|
nnord |
|
38 |
|
nnord |
|
39 |
|
ordtri2 |
|
40 |
37 38 39
|
syl2an |
|
41 |
26 29 40
|
syl2anc |
|
42 |
24 36 41
|
3imtr4d |
|
43 |
42
|
ex |
|
44 |
43
|
com23 |
|
45 |
18 44
|
mpdd |
|
46 |
45 18
|
jcad |
|
47 |
4 46
|
impbid |
|