Step |
Hyp |
Ref |
Expression |
1 |
|
fprodn0f.kph |
|
2 |
|
fprodn0f.a |
|
3 |
|
fprodn0f.b |
|
4 |
|
fprodn0f.bne0 |
|
5 |
|
difssd |
|
6 |
|
eldifi |
|
7 |
6
|
adantr |
|
8 |
|
eldifi |
|
9 |
8
|
adantl |
|
10 |
7 9
|
mulcld |
|
11 |
|
eldifsni |
|
12 |
11
|
adantr |
|
13 |
|
eldifsni |
|
14 |
13
|
adantl |
|
15 |
7 9 12 14
|
mulne0d |
|
16 |
15
|
neneqd |
|
17 |
|
ovex |
|
18 |
17
|
elsn |
|
19 |
16 18
|
sylnibr |
|
20 |
10 19
|
eldifd |
|
21 |
20
|
adantl |
|
22 |
4
|
neneqd |
|
23 |
|
elsng |
|
24 |
3 23
|
syl |
|
25 |
22 24
|
mtbird |
|
26 |
3 25
|
eldifd |
|
27 |
|
ax-1cn |
|
28 |
|
ax-1ne0 |
|
29 |
|
1ex |
|
30 |
29
|
elsn |
|
31 |
28 30
|
nemtbir |
|
32 |
|
eldif |
|
33 |
27 31 32
|
mpbir2an |
|
34 |
33
|
a1i |
|
35 |
1 5 21 2 26 34
|
fprodcllemf |
|
36 |
|
eldifsni |
|
37 |
35 36
|
syl |
|