Step |
Hyp |
Ref |
Expression |
1 |
|
simplll |
|
2 |
|
simpllr |
|
3 |
|
simplrl |
|
4 |
|
simplrr |
|
5 |
|
simpr |
|
6 |
1 2 3 4 5
|
irrdifflemf |
|
7 |
6
|
ex |
|
8 |
7
|
ralrimivva |
|
9 |
|
simplr |
|
10 |
|
peano2rem |
|
11 |
|
recn |
|
12 |
|
1cnd |
|
13 |
11 12
|
negsubd |
|
14 |
|
neg1lt0 |
|
15 |
|
0lt1 |
|
16 |
|
neg1rr |
|
17 |
|
0re |
|
18 |
|
1re |
|
19 |
16 17 18
|
lttri |
|
20 |
14 15 19
|
mp2an |
|
21 |
16
|
a1i |
|
22 |
|
1red |
|
23 |
|
id |
|
24 |
21 22 23
|
ltadd2d |
|
25 |
20 24
|
mpbii |
|
26 |
13 25
|
eqbrtrrd |
|
27 |
10 26
|
ltned |
|
28 |
27
|
ad2antrr |
|
29 |
|
1z |
|
30 |
|
zq |
|
31 |
29 30
|
ax-mp |
|
32 |
|
qsubcl |
|
33 |
31 32
|
mpan2 |
|
34 |
|
qaddcl |
|
35 |
31 34
|
mpan2 |
|
36 |
35
|
adantl |
|
37 |
|
simpl |
|
38 |
|
simpr |
|
39 |
37 38
|
neeq12d |
|
40 |
|
oveq2 |
|
41 |
40
|
adantr |
|
42 |
41
|
fveq2d |
|
43 |
|
oveq2 |
|
44 |
43
|
adantl |
|
45 |
44
|
fveq2d |
|
46 |
42 45
|
neeq12d |
|
47 |
39 46
|
imbi12d |
|
48 |
47
|
rspc2gv |
|
49 |
33 36 48
|
syl2an2 |
|
50 |
9 28 49
|
mp2d |
|
51 |
|
neirr |
|
52 |
11 12
|
nncand |
|
53 |
52
|
fveq2d |
|
54 |
11 12
|
subnegd |
|
55 |
54
|
oveq2d |
|
56 |
21
|
recnd |
|
57 |
11 56
|
nncand |
|
58 |
55 57
|
eqtr3d |
|
59 |
58
|
fveq2d |
|
60 |
12
|
absnegd |
|
61 |
59 60
|
eqtrd |
|
62 |
53 61
|
neeq12d |
|
63 |
51 62
|
mtbiri |
|
64 |
63
|
ad2antrr |
|
65 |
50 64
|
pm2.65da |
|
66 |
8 65
|
impbida |
|