Step |
Hyp |
Ref |
Expression |
1 |
|
qqhval2.0 |
|
2 |
|
qqhval2.1 |
|
3 |
|
qqhval2.2 |
|
4 |
|
elex |
|
5 |
4
|
adantr |
|
6 |
|
eqid |
|
7 |
2 6 3
|
qqhval |
|
8 |
5 7
|
syl |
|
9 |
|
eqidd |
|
10 |
|
eqid |
|
11 |
1 3 10
|
zrhunitpreima |
|
12 |
|
mpoeq12 |
|
13 |
9 11 12
|
syl2anc |
|
14 |
13
|
rneqd |
|
15 |
|
nfv |
|
16 |
|
nfab1 |
|
17 |
|
nfcv |
|
18 |
|
simpr |
|
19 |
|
zssq |
|
20 |
|
simplrl |
|
21 |
19 20
|
sselid |
|
22 |
|
simplrr |
|
23 |
22
|
eldifad |
|
24 |
19 23
|
sselid |
|
25 |
22
|
eldifbd |
|
26 |
|
velsn |
|
27 |
26
|
necon3bbii |
|
28 |
25 27
|
sylib |
|
29 |
|
qdivcl |
|
30 |
21 24 28 29
|
syl3anc |
|
31 |
|
simplll |
|
32 |
|
simpllr |
|
33 |
1 2 3
|
qqhval2lem |
|
34 |
33
|
eqcomd |
|
35 |
31 32 20 23 28 34
|
syl23anc |
|
36 |
|
ovex |
|
37 |
|
ovex |
|
38 |
|
opeq12 |
|
39 |
38
|
eqeq2d |
|
40 |
|
simpl |
|
41 |
40
|
eleq1d |
|
42 |
|
simpr |
|
43 |
40
|
fveq2d |
|
44 |
43
|
fveq2d |
|
45 |
40
|
fveq2d |
|
46 |
45
|
fveq2d |
|
47 |
44 46
|
oveq12d |
|
48 |
42 47
|
eqeq12d |
|
49 |
41 48
|
anbi12d |
|
50 |
39 49
|
anbi12d |
|
51 |
36 37 50
|
spc2ev |
|
52 |
18 30 35 51
|
syl12anc |
|
53 |
52
|
ex |
|
54 |
53
|
rexlimdvva |
|
55 |
54
|
imp |
|
56 |
|
19.42vv |
|
57 |
|
simprrl |
|
58 |
|
qnumcl |
|
59 |
57 58
|
syl |
|
60 |
|
qdencl |
|
61 |
57 60
|
syl |
|
62 |
61
|
nnzd |
|
63 |
|
nnne0 |
|
64 |
|
nelsn |
|
65 |
61 63 64
|
3syl |
|
66 |
62 65
|
eldifd |
|
67 |
|
simprl |
|
68 |
|
qeqnumdivden |
|
69 |
57 68
|
syl |
|
70 |
|
simprrr |
|
71 |
69 70
|
opeq12d |
|
72 |
67 71
|
eqtrd |
|
73 |
|
oveq1 |
|
74 |
|
fveq2 |
|
75 |
74
|
oveq1d |
|
76 |
73 75
|
opeq12d |
|
77 |
76
|
eqeq2d |
|
78 |
|
oveq2 |
|
79 |
|
fveq2 |
|
80 |
79
|
oveq2d |
|
81 |
78 80
|
opeq12d |
|
82 |
81
|
eqeq2d |
|
83 |
77 82
|
rspc2ev |
|
84 |
59 66 72 83
|
syl3anc |
|
85 |
84
|
exlimivv |
|
86 |
56 85
|
sylbir |
|
87 |
55 86
|
impbida |
|
88 |
|
abid |
|
89 |
|
elopab |
|
90 |
87 88 89
|
3bitr4g |
|
91 |
15 16 17 90
|
eqrd |
|
92 |
|
eqid |
|
93 |
92
|
rnmpo |
|
94 |
|
df-mpt |
|
95 |
91 93 94
|
3eqtr4g |
|
96 |
8 14 95
|
3eqtrd |
|