Step |
Hyp |
Ref |
Expression |
1 |
|
fprodcncf.a |
|
2 |
|
fprodcncf.b |
|
3 |
|
fprodcncf.c |
|
4 |
|
fprodcncf.cn |
|
5 |
|
prodeq1 |
|
6 |
5
|
mpteq2dv |
|
7 |
6
|
eleq1d |
|
8 |
|
prodeq1 |
|
9 |
8
|
mpteq2dv |
|
10 |
9
|
eleq1d |
|
11 |
|
prodeq1 |
|
12 |
11
|
mpteq2dv |
|
13 |
12
|
eleq1d |
|
14 |
|
prodeq1 |
|
15 |
14
|
mpteq2dv |
|
16 |
15
|
eleq1d |
|
17 |
|
prod0 |
|
18 |
17
|
a1i |
|
19 |
18
|
mpteq2dv |
|
20 |
|
1cnd |
|
21 |
|
ssidd |
|
22 |
1 20 21
|
constcncfg |
|
23 |
19 22
|
eqeltrd |
|
24 |
|
nfcv |
|
25 |
|
nfcv |
|
26 |
|
nfcsb1v |
|
27 |
25 26
|
nfcprod |
|
28 |
|
csbeq1a |
|
29 |
28
|
adantr |
|
30 |
29
|
prodeq2dv |
|
31 |
24 27 30
|
cbvmpt |
|
32 |
31
|
a1i |
|
33 |
|
nfv |
|
34 |
|
nfcsb1v |
|
35 |
2
|
adantr |
|
36 |
|
simpr |
|
37 |
|
ssfi |
|
38 |
35 36 37
|
syl2anc |
|
39 |
38
|
adantrr |
|
40 |
39
|
adantr |
|
41 |
|
vex |
|
42 |
41
|
a1i |
|
43 |
|
eldifn |
|
44 |
43
|
ad2antll |
|
45 |
44
|
adantr |
|
46 |
|
simplll |
|
47 |
|
simplr |
|
48 |
36
|
adantrr |
|
49 |
48
|
ad2antrr |
|
50 |
|
simpr |
|
51 |
49 50
|
sseldd |
|
52 |
|
nfv |
|
53 |
26
|
nfel1 |
|
54 |
52 53
|
nfim |
|
55 |
|
eleq1w |
|
56 |
55
|
3anbi2d |
|
57 |
28
|
eleq1d |
|
58 |
56 57
|
imbi12d |
|
59 |
54 58 3
|
chvarfv |
|
60 |
46 47 51 59
|
syl3anc |
|
61 |
|
csbeq1a |
|
62 |
|
simpll |
|
63 |
|
eldifi |
|
64 |
63
|
ad2antll |
|
65 |
64
|
adantr |
|
66 |
|
simpr |
|
67 |
|
simpll |
|
68 |
|
simpr |
|
69 |
|
simplr |
|
70 |
|
nfv |
|
71 |
|
nfcv |
|
72 |
34 71
|
nfel |
|
73 |
70 72
|
nfim |
|
74 |
|
eleq1w |
|
75 |
74
|
3anbi3d |
|
76 |
61
|
eleq1d |
|
77 |
75 76
|
imbi12d |
|
78 |
73 77 59
|
chvarfv |
|
79 |
67 68 69 78
|
syl3anc |
|
80 |
62 65 66 79
|
syl21anc |
|
81 |
33 34 40 42 45 60 61 80
|
fprodsplitsn |
|
82 |
81
|
mpteq2dva |
|
83 |
82
|
adantr |
|
84 |
|
nfcv |
|
85 |
|
nfcv |
|
86 |
85 26
|
nfcprod |
|
87 |
28
|
adantr |
|
88 |
87
|
prodeq2dv |
|
89 |
84 86 88
|
cbvmpt |
|
90 |
89
|
eqcomi |
|
91 |
90
|
a1i |
|
92 |
|
id |
|
93 |
91 92
|
eqeltrd |
|
94 |
93
|
adantl |
|
95 |
|
nfv |
|
96 |
|
nfcv |
|
97 |
96 34
|
nfmpt |
|
98 |
|
nfcv |
|
99 |
97 98
|
nfel |
|
100 |
95 99
|
nfim |
|
101 |
74
|
anbi2d |
|
102 |
61
|
adantr |
|
103 |
102
|
mpteq2dva |
|
104 |
103
|
eleq1d |
|
105 |
101 104
|
imbi12d |
|
106 |
|
nfcv |
|
107 |
106 26 28
|
cbvmpt |
|
108 |
107 4
|
eqeltrrid |
|
109 |
100 105 108
|
chvarfv |
|
110 |
64 109
|
syldan |
|
111 |
110
|
adantr |
|
112 |
94 111
|
mulcncf |
|
113 |
83 112
|
eqeltrd |
|
114 |
32 113
|
eqeltrd |
|
115 |
114
|
ex |
|
116 |
7 10 13 16 23 115 2
|
findcard2d |
|