Step |
Hyp |
Ref |
Expression |
1 |
|
en2lp |
|
2 |
|
ianor |
|
3 |
1 2
|
mpbi |
|
4 |
|
sucidg |
|
5 |
|
eleq2 |
|
6 |
4 5
|
syl5ibcom |
|
7 |
|
elsucg |
|
8 |
6 7
|
sylibd |
|
9 |
8
|
imp |
|
10 |
9
|
ord |
|
11 |
10
|
ex |
|
12 |
11
|
com23 |
|
13 |
|
sucidg |
|
14 |
|
eleq2 |
|
15 |
13 14
|
syl5ibrcom |
|
16 |
|
elsucg |
|
17 |
15 16
|
sylibd |
|
18 |
17
|
imp |
|
19 |
18
|
ord |
|
20 |
|
eqcom |
|
21 |
19 20
|
syl6ib |
|
22 |
21
|
ex |
|
23 |
22
|
com23 |
|
24 |
12 23
|
jaao |
|
25 |
3 24
|
mpi |
|
26 |
|
sucexb |
|
27 |
|
sucexb |
|
28 |
27
|
notbii |
|
29 |
|
nelneq |
|
30 |
26 28 29
|
syl2anb |
|
31 |
30
|
pm2.21d |
|
32 |
|
eqcom |
|
33 |
26
|
notbii |
|
34 |
|
nelneq |
|
35 |
27 33 34
|
syl2anb |
|
36 |
35
|
ancoms |
|
37 |
36
|
pm2.21d |
|
38 |
32 37
|
syl5bi |
|
39 |
|
sucprc |
|
40 |
|
sucprc |
|
41 |
39 40
|
eqeqan12d |
|
42 |
41
|
biimpd |
|
43 |
25 31 38 42
|
4cases |
|
44 |
|
suceq |
|
45 |
43 44
|
impbii |
|