Step |
Hyp |
Ref |
Expression |
1 |
|
simplr |
|
2 |
|
simpr |
|
3 |
2
|
oveq1d |
|
4 |
|
xnn0xr |
|
5 |
4
|
ad5antlr |
|
6 |
|
simp-5r |
|
7 |
|
simprr |
|
8 |
7
|
ad3antrrr |
|
9 |
|
xnn0gt0 |
|
10 |
6 8 9
|
syl2anc |
|
11 |
|
xmulpnf2 |
|
12 |
5 10 11
|
syl2anc |
|
13 |
|
pnfnre2 |
|
14 |
|
nn0re |
|
15 |
13 14
|
mto |
|
16 |
15
|
a1i |
|
17 |
12 16
|
eqneltrd |
|
18 |
3 17
|
eqneltrd |
|
19 |
|
simpr |
|
20 |
19
|
oveq2d |
|
21 |
|
xnn0xr |
|
22 |
21
|
ad5antr |
|
23 |
|
simp-5l |
|
24 |
|
simprl |
|
25 |
24
|
ad3antrrr |
|
26 |
|
xnn0gt0 |
|
27 |
23 25 26
|
syl2anc |
|
28 |
|
xmulpnf1 |
|
29 |
22 27 28
|
syl2anc |
|
30 |
15
|
a1i |
|
31 |
29 30
|
eqneltrd |
|
32 |
20 31
|
eqneltrd |
|
33 |
|
xnn0nnn0pnf |
|
34 |
33
|
ad5ant15 |
|
35 |
34
|
ex |
|
36 |
|
xnn0nnn0pnf |
|
37 |
36
|
ad5ant25 |
|
38 |
37
|
ex |
|
39 |
35 38
|
orim12d |
|
40 |
|
pm3.13 |
|
41 |
39 40
|
impel |
|
42 |
18 32 41
|
mpjaodan |
|
43 |
1 42
|
condan |
|
44 |
|
nn0re |
|
45 |
44
|
ad2antrl |
|
46 |
|
nn0re |
|
47 |
46
|
ad2antll |
|
48 |
|
rexmul |
|
49 |
45 47 48
|
syl2anc |
|
50 |
|
nn0mulcl |
|
51 |
50
|
adantl |
|
52 |
49 51
|
eqeltrd |
|
53 |
43 52
|
impbida |
|