Step |
Hyp |
Ref |
Expression |
1 |
|
dssmapfvd.o |
|
2 |
|
dssmapfvd.d |
|
3 |
|
dssmapfvd.b |
|
4 |
|
simpr |
|
5 |
|
difeq2 |
|
6 |
5
|
fveq2d |
|
7 |
6
|
difeq2d |
|
8 |
7
|
cbvmptv |
|
9 |
4 8
|
eqtrdi |
|
10 |
|
ssun1 |
|
11 |
10
|
sspwi |
|
12 |
|
pwidg |
|
13 |
3 12
|
syl |
|
14 |
11 13
|
sseldi |
|
15 |
|
fvex |
|
16 |
15
|
elpwun |
|
17 |
14 16
|
sylib |
|
18 |
17
|
ad2antrr |
|
19 |
9 18
|
fmpt3d |
|
20 |
3
|
pwexd |
|
21 |
20
|
adantr |
|
22 |
21 21
|
elmapd |
|
23 |
19 22
|
mpbird |
|
24 |
23
|
adantrl |
|
25 |
|
simplr |
|
26 |
|
difeq2 |
|
27 |
26
|
fveq2d |
|
28 |
27
|
difeq2d |
|
29 |
28
|
cbvmptv |
|
30 |
25 29
|
eqtrdi |
|
31 |
|
difeq2 |
|
32 |
31
|
fveq2d |
|
33 |
32
|
difeq2d |
|
34 |
33
|
adantl |
|
35 |
|
ssun1 |
|
36 |
35
|
sspwi |
|
37 |
36 13
|
sseldi |
|
38 |
|
vex |
|
39 |
38
|
elpwun |
|
40 |
37 39
|
sylib |
|
41 |
40
|
ad2antrr |
|
42 |
|
difexg |
|
43 |
3 42
|
syl |
|
44 |
43
|
ad2antrr |
|
45 |
30 34 41 44
|
fvmptd |
|
46 |
45
|
difeq2d |
|
47 |
46
|
adantlrl |
|
48 |
|
elpwi |
|
49 |
|
dfss4 |
|
50 |
48 49
|
sylib |
|
51 |
50
|
fveq2d |
|
52 |
51
|
difeq2d |
|
53 |
52
|
difeq2d |
|
54 |
53
|
adantl |
|
55 |
20 20
|
elmapd |
|
56 |
55
|
biimpa |
|
57 |
56
|
ffvelrnda |
|
58 |
57
|
elpwid |
|
59 |
|
dfss4 |
|
60 |
58 59
|
sylib |
|
61 |
60
|
adantlrr |
|
62 |
47 54 61
|
3eqtrrd |
|
63 |
62
|
ralrimiva |
|
64 |
|
elmapfn |
|
65 |
64
|
ad2antrl |
|
66 |
|
difeq2 |
|
67 |
66
|
fveq2d |
|
68 |
67
|
difeq2d |
|
69 |
|
difexg |
|
70 |
3 69
|
syl |
|
71 |
70
|
ad2antrr |
|
72 |
|
difexg |
|
73 |
3 72
|
syl |
|
74 |
73
|
ad2antrr |
|
75 |
65 68 71 74
|
fnmptfvd |
|
76 |
63 75
|
mpbird |
|
77 |
24 76
|
jca |
|
78 |
|
simpr |
|
79 |
|
difeq2 |
|
80 |
79
|
fveq2d |
|
81 |
80
|
difeq2d |
|
82 |
81
|
cbvmptv |
|
83 |
78 82
|
eqtrdi |
|
84 |
|
ssun1 |
|
85 |
84
|
sspwi |
|
86 |
85 13
|
sseldi |
|
87 |
|
fvex |
|
88 |
87
|
elpwun |
|
89 |
86 88
|
sylib |
|
90 |
89
|
ad2antrr |
|
91 |
83 90
|
fmpt3d |
|
92 |
20
|
adantr |
|
93 |
92 92
|
elmapd |
|
94 |
91 93
|
mpbird |
|
95 |
94
|
adantrl |
|
96 |
|
simplr |
|
97 |
|
difeq2 |
|
98 |
97
|
fveq2d |
|
99 |
98
|
difeq2d |
|
100 |
99
|
cbvmptv |
|
101 |
96 100
|
eqtrdi |
|
102 |
31
|
fveq2d |
|
103 |
102
|
difeq2d |
|
104 |
103
|
adantl |
|
105 |
40
|
ad2antrr |
|
106 |
|
difexg |
|
107 |
3 106
|
syl |
|
108 |
107
|
ad2antrr |
|
109 |
101 104 105 108
|
fvmptd |
|
110 |
109
|
difeq2d |
|
111 |
110
|
adantlrl |
|
112 |
50
|
fveq2d |
|
113 |
112
|
difeq2d |
|
114 |
113
|
difeq2d |
|
115 |
114
|
adantl |
|
116 |
20 20
|
elmapd |
|
117 |
116
|
biimpa |
|
118 |
117
|
ffvelrnda |
|
119 |
118
|
elpwid |
|
120 |
|
dfss4 |
|
121 |
119 120
|
sylib |
|
122 |
121
|
adantlrr |
|
123 |
111 115 122
|
3eqtrrd |
|
124 |
123
|
ralrimiva |
|
125 |
|
elmapfn |
|
126 |
125
|
ad2antrl |
|
127 |
|
difeq2 |
|
128 |
127
|
fveq2d |
|
129 |
128
|
difeq2d |
|
130 |
|
difexg |
|
131 |
3 130
|
syl |
|
132 |
131
|
ad2antrr |
|
133 |
|
difexg |
|
134 |
3 133
|
syl |
|
135 |
134
|
ad2antrr |
|
136 |
126 129 132 135
|
fnmptfvd |
|
137 |
124 136
|
mpbird |
|
138 |
95 137
|
jca |
|
139 |
77 138
|
impbida |
|
140 |
139
|
mptcnv |
|
141 |
1 2 3
|
dssmapfvd |
|
142 |
141
|
cnveqd |
|
143 |
|
fveq1 |
|
144 |
143
|
difeq2d |
|
145 |
144
|
mpteq2dv |
|
146 |
|
difeq2 |
|
147 |
146
|
fveq2d |
|
148 |
147
|
difeq2d |
|
149 |
148
|
cbvmptv |
|
150 |
145 149
|
eqtrdi |
|
151 |
150
|
cbvmptv |
|
152 |
151
|
mpteq2i |
|
153 |
1 152
|
eqtri |
|
154 |
153 2 3
|
dssmapfvd |
|
155 |
140 142 154
|
3eqtr4d |
|