Step |
Hyp |
Ref |
Expression |
1 |
|
cntzrec.b |
|
2 |
|
cntzrec.z |
|
3 |
1 2
|
cntzssv |
|
4 |
3
|
a1i |
|
5 |
|
eqid |
|
6 |
1 5
|
mndidcl |
|
7 |
6
|
adantr |
|
8 |
|
simpll |
|
9 |
|
simpr |
|
10 |
9
|
sselda |
|
11 |
|
eqid |
|
12 |
1 11 5
|
mndlid |
|
13 |
8 10 12
|
syl2anc |
|
14 |
1 11 5
|
mndrid |
|
15 |
8 10 14
|
syl2anc |
|
16 |
13 15
|
eqtr4d |
|
17 |
16
|
ralrimiva |
|
18 |
1 11 2
|
elcntz |
|
19 |
18
|
adantl |
|
20 |
7 17 19
|
mpbir2and |
|
21 |
|
simpll |
|
22 |
|
simprl |
|
23 |
3 22
|
sseldi |
|
24 |
|
simprr |
|
25 |
3 24
|
sseldi |
|
26 |
1 11
|
mndcl |
|
27 |
21 23 25 26
|
syl3anc |
|
28 |
21
|
adantr |
|
29 |
23
|
adantr |
|
30 |
25
|
adantr |
|
31 |
10
|
adantlr |
|
32 |
1 11
|
mndass |
|
33 |
28 29 30 31 32
|
syl13anc |
|
34 |
11 2
|
cntzi |
|
35 |
24 34
|
sylan |
|
36 |
35
|
oveq2d |
|
37 |
1 11
|
mndass |
|
38 |
28 29 31 30 37
|
syl13anc |
|
39 |
11 2
|
cntzi |
|
40 |
22 39
|
sylan |
|
41 |
40
|
oveq1d |
|
42 |
36 38 41
|
3eqtr2d |
|
43 |
1 11
|
mndass |
|
44 |
28 31 29 30 43
|
syl13anc |
|
45 |
33 42 44
|
3eqtrd |
|
46 |
45
|
ralrimiva |
|
47 |
1 11 2
|
elcntz |
|
48 |
47
|
ad2antlr |
|
49 |
27 46 48
|
mpbir2and |
|
50 |
49
|
ralrimivva |
|
51 |
1 5 11
|
issubm |
|
52 |
51
|
adantr |
|
53 |
4 20 50 52
|
mpbir3and |
|