Step |
Hyp |
Ref |
Expression |
1 |
|
2re |
|
2 |
|
1re |
|
3 |
|
ltsub1 |
|
4 |
1 2 3
|
mp3an13 |
|
5 |
|
2m1e1 |
|
6 |
5
|
breq1i |
|
7 |
4 6
|
bitrdi |
|
8 |
|
ltsub1 |
|
9 |
1 2 8
|
mp3an13 |
|
10 |
5
|
breq1i |
|
11 |
9 10
|
bitrdi |
|
12 |
7 11
|
bi2anan9 |
|
13 |
|
peano2rem |
|
14 |
|
peano2rem |
|
15 |
|
mulgt1 |
|
16 |
15
|
ex |
|
17 |
13 14 16
|
syl2an |
|
18 |
12 17
|
sylbid |
|
19 |
|
recn |
|
20 |
|
recn |
|
21 |
|
ax-1cn |
|
22 |
|
mulsub |
|
23 |
21 22
|
mpanl2 |
|
24 |
21 23
|
mpanr2 |
|
25 |
19 20 24
|
syl2an |
|
26 |
25
|
breq2d |
|
27 |
|
remulcl |
|
28 |
2 27
|
mpan2 |
|
29 |
|
remulcl |
|
30 |
2 29
|
mpan2 |
|
31 |
|
readdcl |
|
32 |
28 30 31
|
syl2an |
|
33 |
|
remulcl |
|
34 |
2 2
|
remulcli |
|
35 |
|
readdcl |
|
36 |
33 34 35
|
sylancl |
|
37 |
|
ltaddsub2 |
|
38 |
2 37
|
mp3an2 |
|
39 |
32 36 38
|
syl2anc |
|
40 |
|
1t1e1 |
|
41 |
40
|
oveq2i |
|
42 |
41
|
breq2i |
|
43 |
39 42
|
bitr3di |
|
44 |
|
ltadd1 |
|
45 |
2 44
|
mp3an3 |
|
46 |
32 33 45
|
syl2anc |
|
47 |
|
ax-1rid |
|
48 |
|
ax-1rid |
|
49 |
47 48
|
oveqan12d |
|
50 |
49
|
breq1d |
|
51 |
46 50
|
bitr3d |
|
52 |
26 43 51
|
3bitrd |
|
53 |
18 52
|
sylibd |
|
54 |
53
|
imp |
|