Step |
Hyp |
Ref |
Expression |
1 |
|
usgr2pthlem.v |
|
2 |
|
usgr2pthlem.i |
|
3 |
|
usgr2pthspth |
|
4 |
|
usgrupgr |
|
5 |
4
|
adantr |
|
6 |
|
isspth |
|
7 |
6
|
a1i |
|
8 |
1 2
|
upgrf1istrl |
|
9 |
8
|
anbi1d |
|
10 |
|
oveq2 |
|
11 |
|
f1eq2 |
|
12 |
10 11
|
syl |
|
13 |
12
|
biimpd |
|
14 |
13
|
adantl |
|
15 |
14
|
com12 |
|
16 |
15
|
3ad2ant1 |
|
17 |
16
|
ad2antrl |
|
18 |
|
oveq2 |
|
19 |
18
|
feq2d |
|
20 |
|
df-f1 |
|
21 |
20
|
simplbi2 |
|
22 |
21
|
a1i |
|
23 |
19 22
|
sylbid |
|
24 |
23
|
adantl |
|
25 |
24
|
com3l |
|
26 |
25
|
3ad2ant2 |
|
27 |
26
|
imp |
|
28 |
27
|
adantl |
|
29 |
1 2
|
usgr2pthlem |
|
30 |
29
|
ad2antrl |
|
31 |
17 28 30
|
3jcad |
|
32 |
31
|
ex |
|
33 |
9 32
|
sylbid |
|
34 |
7 33
|
sylbid |
|
35 |
34
|
com23 |
|
36 |
5 35
|
mpcom |
|
37 |
3 36
|
sylbid |
|
38 |
37
|
ex |
|
39 |
38
|
impcomd |
|
40 |
|
2nn0 |
|
41 |
|
f1f |
|
42 |
|
fnfzo0hash |
|
43 |
40 41 42
|
sylancr |
|
44 |
|
oveq2 |
|
45 |
44
|
eqcoms |
|
46 |
|
f1eq2 |
|
47 |
45 46
|
syl |
|
48 |
47
|
biimpd |
|
49 |
48
|
imp |
|
50 |
49
|
adantr |
|
51 |
50
|
ad2antrr |
|
52 |
|
f1f |
|
53 |
|
oveq2 |
|
54 |
53
|
eqcoms |
|
55 |
54
|
adantr |
|
56 |
55
|
feq2d |
|
57 |
52 56
|
syl5ib |
|
58 |
57
|
imp |
|
59 |
58
|
ad2antrr |
|
60 |
|
eqcom |
|
61 |
60
|
biimpi |
|
62 |
61
|
3ad2ant1 |
|
63 |
|
eqcom |
|
64 |
63
|
biimpi |
|
65 |
64
|
3ad2ant2 |
|
66 |
62 65
|
preq12d |
|
67 |
66
|
eqeq2d |
|
68 |
67
|
biimpcd |
|
69 |
68
|
adantr |
|
70 |
69
|
impcom |
|
71 |
|
eqcom |
|
72 |
71
|
biimpi |
|
73 |
72
|
3ad2ant3 |
|
74 |
65 73
|
preq12d |
|
75 |
74
|
eqeq2d |
|
76 |
75
|
biimpcd |
|
77 |
76
|
adantl |
|
78 |
77
|
impcom |
|
79 |
70 78
|
jca |
|
80 |
79
|
rexlimivw |
|
81 |
80
|
rexlimivw |
|
82 |
81
|
rexlimivw |
|
83 |
82
|
a1i13 |
|
84 |
|
fzo0to2pr |
|
85 |
10 84
|
eqtrdi |
|
86 |
85
|
raleqdv |
|
87 |
|
2wlklem |
|
88 |
86 87
|
syl6bb |
|
89 |
88
|
imbi2d |
|
90 |
83 89
|
sylibrd |
|
91 |
90
|
ad2antrr |
|
92 |
91
|
imp |
|
93 |
92
|
imp |
|
94 |
51 59 93
|
3jca |
|
95 |
20
|
simprbi |
|
96 |
95
|
adantl |
|
97 |
96
|
ad2antrr |
|
98 |
94 97
|
jca |
|
99 |
7 9
|
bitrd |
|
100 |
4 99
|
syl |
|
101 |
100
|
adantl |
|
102 |
98 101
|
mpbird |
|
103 |
|
simpr |
|
104 |
|
simp-4l |
|
105 |
103 104 3
|
syl2anc |
|
106 |
102 105
|
mpbird |
|
107 |
106 104
|
jca |
|
108 |
107
|
ex |
|
109 |
108
|
exp41 |
|
110 |
43 109
|
mpcom |
|
111 |
110
|
3imp |
|
112 |
111
|
com12 |
|
113 |
39 112
|
impbid |
|