Step |
Hyp |
Ref |
Expression |
1 |
|
2cnd |
|
2 |
|
simpr |
|
3 |
|
simpr |
|
4 |
3
|
adantr |
|
5 |
2 4
|
nn0addcld |
|
6 |
5
|
nn0cnd |
|
7 |
|
2nn0 |
|
8 |
7
|
a1i |
|
9 |
|
id |
|
10 |
8 9
|
nn0expcld |
|
11 |
10
|
nn0cnd |
|
12 |
11
|
ad2antrr |
|
13 |
6 12
|
mulcld |
|
14 |
|
nn0cn |
|
15 |
14
|
ad2antlr |
|
16 |
1 13 15
|
subdid |
|
17 |
16
|
oveq1d |
|
18 |
7
|
a1i |
|
19 |
10
|
ad2antrr |
|
20 |
5 19
|
nn0mulcld |
|
21 |
18 20
|
nn0mulcld |
|
22 |
21
|
nn0cnd |
|
23 |
7
|
a1i |
|
24 |
23 3
|
nn0mulcld |
|
25 |
24
|
adantr |
|
26 |
25
|
nn0cnd |
|
27 |
4
|
nn0cnd |
|
28 |
22 26 27
|
subsubd |
|
29 |
1 6 12
|
mul12d |
|
30 |
|
2cnd |
|
31 |
30 11
|
mulcomd |
|
32 |
30 9
|
expp1d |
|
33 |
31 32
|
eqtr4d |
|
34 |
33
|
ad2antrr |
|
35 |
34
|
oveq2d |
|
36 |
29 35
|
eqtrd |
|
37 |
|
2txmxeqx |
|
38 |
14 37
|
syl |
|
39 |
38
|
ad2antlr |
|
40 |
36 39
|
oveq12d |
|
41 |
17 28 40
|
3eqtr2d |
|