Step |
Hyp |
Ref |
Expression |
1 |
|
2sq |
|
2 |
|
elnn0z |
|
3 |
2
|
biimpri |
|
4 |
|
elznn0 |
|
5 |
|
nn0ge0 |
|
6 |
5
|
pm2.24d |
|
7 |
6
|
a1i |
|
8 |
|
ax-1 |
|
9 |
8
|
a1i |
|
10 |
7 9
|
jaod |
|
11 |
10
|
imp |
|
12 |
4 11
|
sylbi |
|
13 |
12
|
imp |
|
14 |
3 13
|
ifclda |
|
15 |
14
|
adantr |
|
16 |
15
|
adantr |
|
17 |
|
elnn0z |
|
18 |
17
|
biimpri |
|
19 |
|
elznn0 |
|
20 |
|
nn0ge0 |
|
21 |
20
|
pm2.24d |
|
22 |
21
|
a1i |
|
23 |
|
ax-1 |
|
24 |
23
|
a1i |
|
25 |
22 24
|
jaod |
|
26 |
25
|
imp |
|
27 |
19 26
|
sylbi |
|
28 |
27
|
imp |
|
29 |
18 28
|
ifclda |
|
30 |
29
|
adantl |
|
31 |
30
|
adantr |
|
32 |
|
elznn0nn |
|
33 |
5
|
iftrued |
|
34 |
33
|
eqcomd |
|
35 |
34
|
oveq1d |
|
36 |
|
elnnz |
|
37 |
|
lt0neg1 |
|
38 |
|
id |
|
39 |
|
0red |
|
40 |
38 39
|
ltnled |
|
41 |
40
|
biimpd |
|
42 |
37 41
|
sylbird |
|
43 |
42
|
com12 |
|
44 |
36 43
|
simplbiim |
|
45 |
44
|
impcom |
|
46 |
45
|
iffalsed |
|
47 |
46
|
oveq1d |
|
48 |
|
recn |
|
49 |
|
sqneg |
|
50 |
48 49
|
syl |
|
51 |
50
|
adantr |
|
52 |
47 51
|
eqtr2d |
|
53 |
35 52
|
jaoi |
|
54 |
32 53
|
sylbi |
|
55 |
|
elznn0nn |
|
56 |
20
|
iftrued |
|
57 |
56
|
eqcomd |
|
58 |
57
|
oveq1d |
|
59 |
|
elnnz |
|
60 |
|
lt0neg1 |
|
61 |
|
id |
|
62 |
|
0red |
|
63 |
61 62
|
ltnled |
|
64 |
63
|
biimpd |
|
65 |
60 64
|
sylbird |
|
66 |
65
|
com12 |
|
67 |
59 66
|
simplbiim |
|
68 |
67
|
impcom |
|
69 |
68
|
iffalsed |
|
70 |
69
|
oveq1d |
|
71 |
|
recn |
|
72 |
|
sqneg |
|
73 |
71 72
|
syl |
|
74 |
73
|
adantr |
|
75 |
70 74
|
eqtr2d |
|
76 |
58 75
|
jaoi |
|
77 |
55 76
|
sylbi |
|
78 |
54 77
|
oveqan12d |
|
79 |
78
|
eqeq2d |
|
80 |
79
|
biimpd |
|
81 |
80
|
imp |
|
82 |
|
oveq1 |
|
83 |
82
|
oveq1d |
|
84 |
83
|
eqeq2d |
|
85 |
|
oveq1 |
|
86 |
85
|
oveq2d |
|
87 |
86
|
eqeq2d |
|
88 |
84 87
|
rspc2ev |
|
89 |
16 31 81 88
|
syl3anc |
|
90 |
89
|
ex |
|
91 |
90
|
rexlimivv |
|
92 |
1 91
|
syl |
|