Step |
Hyp |
Ref |
Expression |
1 |
|
submateqlem1.n |
|
2 |
|
submateqlem1.k |
|
3 |
|
submateqlem1.m |
|
4 |
|
submateqlem1.1 |
|
5 |
|
fz1ssnn |
|
6 |
5 3
|
sseldi |
|
7 |
6
|
nnred |
|
8 |
1
|
nnred |
|
9 |
|
1red |
|
10 |
8 9
|
resubcld |
|
11 |
|
elfzle2 |
|
12 |
3 11
|
syl |
|
13 |
8
|
lem1d |
|
14 |
7 10 8 12 13
|
letrd |
|
15 |
4 14
|
jca |
|
16 |
6
|
nnzd |
|
17 |
|
fz1ssnn |
|
18 |
17 2
|
sseldi |
|
19 |
18
|
nnzd |
|
20 |
1
|
nnzd |
|
21 |
|
elfz |
|
22 |
16 19 20 21
|
syl3anc |
|
23 |
15 22
|
mpbird |
|
24 |
6
|
nnnn0d |
|
25 |
24
|
nn0ge0d |
|
26 |
|
1re |
|
27 |
|
addge02 |
|
28 |
26 7 27
|
sylancr |
|
29 |
25 28
|
mpbid |
|
30 |
1
|
nnnn0d |
|
31 |
|
nn0ltlem1 |
|
32 |
24 30 31
|
syl2anc |
|
33 |
12 32
|
mpbird |
|
34 |
|
nnltp1le |
|
35 |
6 1 34
|
syl2anc |
|
36 |
33 35
|
mpbid |
|
37 |
29 36
|
jca |
|
38 |
16
|
peano2zd |
|
39 |
|
1zzd |
|
40 |
|
elfz |
|
41 |
38 39 20 40
|
syl3anc |
|
42 |
37 41
|
mpbird |
|
43 |
18
|
nnred |
|
44 |
|
nnleltp1 |
|
45 |
18 6 44
|
syl2anc |
|
46 |
4 45
|
mpbid |
|
47 |
43 46
|
ltned |
|
48 |
47
|
necomd |
|
49 |
|
nelsn |
|
50 |
48 49
|
syl |
|
51 |
42 50
|
eldifd |
|
52 |
23 51
|
jca |
|