Step |
Hyp |
Ref |
Expression |
1 |
|
pmatcollpw.p |
|
2 |
|
pmatcollpw.c |
|
3 |
|
pmatcollpw.b |
|
4 |
|
pmatcollpw.m |
|
5 |
|
pmatcollpw.e |
|
6 |
|
pmatcollpw.x |
|
7 |
|
pmatcollpw.t |
|
8 |
|
pmatcollpw3.a |
|
9 |
|
pmatcollpw3.d |
|
10 |
|
dmeq |
|
11 |
10
|
dmeqd |
|
12 |
|
oveq |
|
13 |
12
|
fveq2d |
|
14 |
13
|
fveq1d |
|
15 |
11 11 14
|
mpoeq123dv |
|
16 |
|
fveq2 |
|
17 |
16
|
mpoeq3dv |
|
18 |
15 17
|
cbvmpov |
|
19 |
|
dmexg |
|
20 |
19
|
dmexd |
|
21 |
20 20
|
jca |
|
22 |
21
|
ad2antrl |
|
23 |
|
mpoexga |
|
24 |
22 23
|
syl |
|
25 |
24
|
ralrimivva |
|
26 |
|
simprr |
|
27 |
|
nn0ex |
|
28 |
27
|
ssex |
|
29 |
28
|
ad2antrl |
|
30 |
|
simp3 |
|
31 |
30
|
adantr |
|
32 |
18 25 26 29 31
|
mpocurryvald |
|
33 |
|
fveq2 |
|
34 |
33
|
mpoeq3dv |
|
35 |
34
|
csbeq2dv |
|
36 |
|
eqcom |
|
37 |
|
eqcom |
|
38 |
15 36 37
|
3imtr3i |
|
39 |
38
|
cbvcsbv |
|
40 |
35 39
|
eqtrdi |
|
41 |
40
|
cbvmptv |
|
42 |
32 41
|
eqtrdi |
|
43 |
|
dmeq |
|
44 |
43
|
dmeqd |
|
45 |
|
oveq |
|
46 |
45
|
fveq2d |
|
47 |
46
|
fveq1d |
|
48 |
44 44 47
|
mpoeq123dv |
|
49 |
48
|
adantl |
|
50 |
30 49
|
csbied |
|
51 |
|
eqid |
|
52 |
2 51 3
|
matbas2i |
|
53 |
|
elmapi |
|
54 |
|
fdm |
|
55 |
54
|
dmeqd |
|
56 |
|
dmxpid |
|
57 |
55 56
|
eqtr2di |
|
58 |
52 53 57
|
3syl |
|
59 |
58
|
3ad2ant3 |
|
60 |
59
|
adantr |
|
61 |
|
simpr |
|
62 |
61
|
oveqd |
|
63 |
62
|
fveq2d |
|
64 |
63
|
fveq1d |
|
65 |
60 60 64
|
mpoeq123dv |
|
66 |
30 65
|
csbied |
|
67 |
50 66
|
eqtr4d |
|
68 |
67
|
adantr |
|
69 |
68
|
mpteq2dv |
|
70 |
42 69
|
eqtrd |
|
71 |
|
oveq |
|
72 |
71
|
adantl |
|
73 |
72
|
fveq2d |
|
74 |
73
|
fveq1d |
|
75 |
74
|
mpoeq3dv |
|
76 |
30 75
|
csbied |
|
77 |
76
|
ad2antrr |
|
78 |
|
eqid |
|
79 |
|
simpll1 |
|
80 |
|
simpll2 |
|
81 |
|
simp2 |
|
82 |
|
simp3 |
|
83 |
31
|
adantr |
|
84 |
83
|
3ad2ant1 |
|
85 |
2 51 3 81 82 84
|
matecld |
|
86 |
|
ssel |
|
87 |
86
|
ad2antrl |
|
88 |
87
|
imp |
|
89 |
88
|
3ad2ant1 |
|
90 |
|
eqid |
|
91 |
90 51 1 78
|
coe1fvalcl |
|
92 |
85 89 91
|
syl2anc |
|
93 |
8 78 9 79 80 92
|
matbas2d |
|
94 |
77 93
|
eqeltrd |
|
95 |
94
|
fmpttd |
|
96 |
9
|
fvexi |
|
97 |
96
|
a1i |
|
98 |
28
|
adantr |
|
99 |
|
elmapg |
|
100 |
97 98 99
|
syl2an |
|
101 |
95 100
|
mpbird |
|
102 |
70 101
|
eqeltrd |
|
103 |
|
fveq1 |
|
104 |
103
|
adantl |
|
105 |
104
|
adantr |
|
106 |
|
eqid |
|
107 |
|
dmexg |
|
108 |
107
|
dmexd |
|
109 |
108 108
|
jca |
|
110 |
109
|
ad2antrl |
|
111 |
|
mpoexga |
|
112 |
110 111
|
syl |
|
113 |
112
|
ralrimivva |
|
114 |
29
|
adantr |
|
115 |
31
|
adantr |
|
116 |
|
simpr |
|
117 |
106 113 114 115 116
|
fvmpocurryd |
|
118 |
|
df-decpmat |
|
119 |
118
|
reseq1i |
|
120 |
|
ssv |
|
121 |
120
|
a1i |
|
122 |
|
simpl |
|
123 |
121 122
|
anim12i |
|
124 |
123
|
adantr |
|
125 |
|
resmpo |
|
126 |
124 125
|
syl |
|
127 |
119 126
|
syl5req |
|
128 |
127
|
oveqd |
|
129 |
117 128
|
eqtrd |
|
130 |
129
|
adantlr |
|
131 |
105 130
|
eqtrd |
|
132 |
131
|
fveq2d |
|
133 |
30
|
ad2antrr |
|
134 |
|
ovres |
|
135 |
133 134
|
sylan |
|
136 |
135
|
fveq2d |
|
137 |
132 136
|
eqtrd |
|
138 |
137
|
oveq2d |
|
139 |
138
|
mpteq2dva |
|
140 |
139
|
oveq2d |
|
141 |
140
|
eqeq2d |
|
142 |
102 141
|
rspcedv |
|