Step |
Hyp |
Ref |
Expression |
1 |
|
smodm2 |
|
2 |
|
simprl |
|
3 |
|
ordelord |
|
4 |
1 2 3
|
syl2an2r |
|
5 |
|
simprr |
|
6 |
|
ordelord |
|
7 |
1 5 6
|
syl2an2r |
|
8 |
|
ordtri3or |
|
9 |
|
simp3 |
|
10 |
|
smoel2 |
|
11 |
10
|
expr |
|
12 |
11
|
adantrl |
|
13 |
12
|
3impia |
|
14 |
9 13
|
2thd |
|
15 |
14
|
3expia |
|
16 |
|
ordirr |
|
17 |
4 16
|
syl |
|
18 |
17
|
3adant3 |
|
19 |
|
simp3 |
|
20 |
18 19
|
neleqtrd |
|
21 |
|
smofvon2 |
|
22 |
21
|
ad2antlr |
|
23 |
|
eloni |
|
24 |
|
ordirr |
|
25 |
22 23 24
|
3syl |
|
26 |
25
|
3adant3 |
|
27 |
19
|
fveq2d |
|
28 |
26 27
|
neleqtrd |
|
29 |
20 28
|
2falsed |
|
30 |
29
|
3expia |
|
31 |
7
|
3adant3 |
|
32 |
|
ordn2lp |
|
33 |
31 32
|
syl |
|
34 |
|
pm3.2 |
|
35 |
34
|
3ad2ant3 |
|
36 |
33 35
|
mtod |
|
37 |
22 23
|
syl |
|
38 |
37
|
3adant3 |
|
39 |
|
ordn2lp |
|
40 |
38 39
|
syl |
|
41 |
|
smoel2 |
|
42 |
41
|
adantrlr |
|
43 |
42
|
3impb |
|
44 |
|
pm3.21 |
|
45 |
43 44
|
syl |
|
46 |
40 45
|
mtod |
|
47 |
36 46
|
2falsed |
|
48 |
47
|
3expia |
|
49 |
15 30 48
|
3jaod |
|
50 |
8 49
|
syl5 |
|
51 |
4 7 50
|
mp2and |
|