Step |
Hyp |
Ref |
Expression |
1 |
|
fprodss.1 |
|
2 |
|
fprodss.2 |
|
3 |
|
fprodss.3 |
|
4 |
|
fprodss.4 |
|
5 |
|
sseq2 |
|
6 |
|
ss0 |
|
7 |
5 6
|
syl6bi |
|
8 |
|
prodeq1 |
|
9 |
|
prodeq1 |
|
10 |
9
|
eqcomd |
|
11 |
8 10
|
sylan9eq |
|
12 |
11
|
expcom |
|
13 |
7 12
|
syld |
|
14 |
1 13
|
syl5com |
|
15 |
|
cnvimass |
|
16 |
|
simprr |
|
17 |
|
f1of |
|
18 |
16 17
|
syl |
|
19 |
15 18
|
fssdm |
|
20 |
|
f1ofn |
|
21 |
|
elpreima |
|
22 |
16 20 21
|
3syl |
|
23 |
18
|
ffvelrnda |
|
24 |
23
|
ex |
|
25 |
24
|
adantrd |
|
26 |
22 25
|
sylbid |
|
27 |
26
|
imp |
|
28 |
2
|
ex |
|
29 |
28
|
adantr |
|
30 |
|
eldif |
|
31 |
|
ax-1cn |
|
32 |
3 31
|
eqeltrdi |
|
33 |
30 32
|
sylan2br |
|
34 |
33
|
expr |
|
35 |
29 34
|
pm2.61d |
|
36 |
35
|
adantlr |
|
37 |
36
|
fmpttd |
|
38 |
37
|
ffvelrnda |
|
39 |
27 38
|
syldan |
|
40 |
|
eqid |
|
41 |
|
simprl |
|
42 |
|
nnuz |
|
43 |
41 42
|
eleqtrdi |
|
44 |
|
ssidd |
|
45 |
40 43 44
|
fprodntriv |
|
46 |
|
eldifi |
|
47 |
46 23
|
sylan2 |
|
48 |
|
eldifn |
|
49 |
48
|
adantl |
|
50 |
46
|
adantl |
|
51 |
22
|
adantr |
|
52 |
50 51
|
mpbirand |
|
53 |
49 52
|
mtbid |
|
54 |
47 53
|
eldifd |
|
55 |
|
difss |
|
56 |
|
resmpt |
|
57 |
55 56
|
ax-mp |
|
58 |
57
|
fveq1i |
|
59 |
|
fvres |
|
60 |
58 59
|
syl5eqr |
|
61 |
54 60
|
syl |
|
62 |
|
1ex |
|
63 |
62
|
elsn2 |
|
64 |
3 63
|
sylibr |
|
65 |
64
|
fmpttd |
|
66 |
65
|
ad2antrr |
|
67 |
66 54
|
ffvelrnd |
|
68 |
|
elsni |
|
69 |
67 68
|
syl |
|
70 |
61 69
|
eqtr3d |
|
71 |
|
fzssuz |
|
72 |
71
|
a1i |
|
73 |
19 39 45 70 72
|
prodss |
|
74 |
1
|
adantr |
|
75 |
74
|
resmptd |
|
76 |
75
|
fveq1d |
|
77 |
|
fvres |
|
78 |
76 77
|
sylan9req |
|
79 |
78
|
prodeq2dv |
|
80 |
|
fveq2 |
|
81 |
|
fzfid |
|
82 |
81 18
|
fisuppfi |
|
83 |
|
f1of1 |
|
84 |
16 83
|
syl |
|
85 |
|
f1ores |
|
86 |
84 19 85
|
syl2anc |
|
87 |
|
f1ofo |
|
88 |
16 87
|
syl |
|
89 |
|
foimacnv |
|
90 |
88 74 89
|
syl2anc |
|
91 |
90
|
f1oeq3d |
|
92 |
86 91
|
mpbid |
|
93 |
|
fvres |
|
94 |
93
|
adantl |
|
95 |
74
|
sselda |
|
96 |
37
|
ffvelrnda |
|
97 |
95 96
|
syldan |
|
98 |
80 82 92 94 97
|
fprodf1o |
|
99 |
79 98
|
eqtrd |
|
100 |
|
eqidd |
|
101 |
80 81 16 100 96
|
fprodf1o |
|
102 |
73 99 101
|
3eqtr4d |
|
103 |
|
prodfc |
|
104 |
|
prodfc |
|
105 |
102 103 104
|
3eqtr3g |
|
106 |
105
|
expr |
|
107 |
106
|
exlimdv |
|
108 |
107
|
expimpd |
|
109 |
|
fz1f1o |
|
110 |
4 109
|
syl |
|
111 |
14 108 110
|
mpjaod |
|