Step |
Hyp |
Ref |
Expression |
1 |
|
fprodser.1 |
|
2 |
|
fprodser.2 |
|
3 |
|
fprodser.3 |
|
4 |
|
prodfc |
|
5 |
|
fveq2 |
|
6 |
|
eluzelz |
|
7 |
2 6
|
syl |
|
8 |
7
|
zcnd |
|
9 |
|
eluzel2 |
|
10 |
2 9
|
syl |
|
11 |
10
|
zcnd |
|
12 |
|
1cnd |
|
13 |
8 11 12
|
subadd23d |
|
14 |
13
|
eqcomd |
|
15 |
|
uznn0sub |
|
16 |
2 15
|
syl |
|
17 |
|
nn0p1nn |
|
18 |
16 17
|
syl |
|
19 |
14 18
|
eqeltrd |
|
20 |
12 11
|
pncan3d |
|
21 |
8 12 11
|
pnpncand |
|
22 |
20 21
|
oveq12d |
|
23 |
22
|
eleq2d |
|
24 |
23
|
biimpa |
|
25 |
|
elfzelz |
|
26 |
25
|
zcnd |
|
27 |
26
|
adantl |
|
28 |
|
peano2zm |
|
29 |
10 28
|
syl |
|
30 |
29
|
zcnd |
|
31 |
30
|
adantr |
|
32 |
27 31
|
npcand |
|
33 |
|
simpr |
|
34 |
32 33
|
eqeltrd |
|
35 |
|
ovex |
|
36 |
|
oveq1 |
|
37 |
36
|
eleq1d |
|
38 |
35 37
|
sbcie |
|
39 |
34 38
|
sylibr |
|
40 |
24 39
|
syldan |
|
41 |
40
|
ralrimiva |
|
42 |
|
1zzd |
|
43 |
19
|
nnzd |
|
44 |
|
fzshftral |
|
45 |
42 43 29 44
|
syl3anc |
|
46 |
41 45
|
mpbird |
|
47 |
10
|
adantr |
|
48 |
7
|
adantr |
|
49 |
25
|
adantl |
|
50 |
29
|
adantr |
|
51 |
|
fzsubel |
|
52 |
47 48 49 50 51
|
syl22anc |
|
53 |
33 52
|
mpbid |
|
54 |
11 12
|
nncand |
|
55 |
8 11 12
|
subsub2d |
|
56 |
54 55
|
oveq12d |
|
57 |
56
|
adantr |
|
58 |
53 57
|
eleqtrd |
|
59 |
32
|
eqcomd |
|
60 |
36
|
rspceeqv |
|
61 |
58 59 60
|
syl2anc |
|
62 |
|
elfzelz |
|
63 |
62
|
zcnd |
|
64 |
|
elfzelz |
|
65 |
64
|
zcnd |
|
66 |
63 65
|
anim12i |
|
67 |
|
eqtr2 |
|
68 |
|
simprl |
|
69 |
|
simprr |
|
70 |
30
|
adantr |
|
71 |
68 69 70
|
addcan2d |
|
72 |
67 71
|
syl5ib |
|
73 |
66 72
|
sylan2 |
|
74 |
73
|
ralrimivva |
|
75 |
74
|
adantr |
|
76 |
|
oveq1 |
|
77 |
76
|
eqeq2d |
|
78 |
77
|
reu4 |
|
79 |
61 75 78
|
sylanbrc |
|
80 |
79
|
ralrimiva |
|
81 |
|
eqid |
|
82 |
81
|
f1ompt |
|
83 |
46 80 82
|
sylanbrc |
|
84 |
3
|
fmpttd |
|
85 |
84
|
ffvelrnda |
|
86 |
|
simpr |
|
87 |
|
1zzd |
|
88 |
43
|
adantr |
|
89 |
64
|
adantl |
|
90 |
29
|
adantr |
|
91 |
|
fzaddel |
|
92 |
87 88 89 90 91
|
syl22anc |
|
93 |
86 92
|
mpbid |
|
94 |
22
|
adantr |
|
95 |
93 94
|
eleqtrd |
|
96 |
1
|
ralrimiva |
|
97 |
|
nfcsb1v |
|
98 |
97
|
nfeq2 |
|
99 |
|
fveq2 |
|
100 |
|
csbeq1a |
|
101 |
99 100
|
eqeq12d |
|
102 |
98 101
|
rspc |
|
103 |
96 102
|
mpan9 |
|
104 |
95 103
|
syldan |
|
105 |
|
f1of |
|
106 |
83 105
|
syl |
|
107 |
|
fvco3 |
|
108 |
106 107
|
sylan |
|
109 |
|
ovex |
|
110 |
76 81 109
|
fvmpt |
|
111 |
110
|
adantl |
|
112 |
111
|
fveq2d |
|
113 |
108 112
|
eqtrd |
|
114 |
111
|
fveq2d |
|
115 |
3
|
ralrimiva |
|
116 |
97
|
nfel1 |
|
117 |
100
|
eleq1d |
|
118 |
116 117
|
rspc |
|
119 |
115 118
|
mpan9 |
|
120 |
95 119
|
syldan |
|
121 |
|
eqid |
|
122 |
121
|
fvmpts |
|
123 |
95 120 122
|
syl2anc |
|
124 |
114 123
|
eqtrd |
|
125 |
104 113 124
|
3eqtr4d |
|
126 |
5 19 83 85 125
|
fprod |
|
127 |
|
nnuz |
|
128 |
19 127
|
eleqtrdi |
|
129 |
128 29 113
|
seqshft2 |
|
130 |
20
|
seqeq1d |
|
131 |
130 21
|
fveq12d |
|
132 |
126 129 131
|
3eqtrd |
|
133 |
4 132
|
syl5eqr |
|