Step |
Hyp |
Ref |
Expression |
1 |
|
hspmbl.1 |
|
2 |
|
hspmbl.x |
|
3 |
|
hspmbl.i |
|
4 |
|
hspmbl.y |
|
5 |
2
|
ovnome |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
|
ovex |
|
9 |
|
reex |
|
10 |
8 9
|
ifex |
|
11 |
10
|
ixpssmap |
|
12 |
|
iftrue |
|
13 |
|
ioossre |
|
14 |
13
|
a1i |
|
15 |
12 14
|
eqsstrd |
|
16 |
|
iffalse |
|
17 |
|
ssid |
|
18 |
17
|
a1i |
|
19 |
16 18
|
eqsstrd |
|
20 |
15 19
|
pm2.61i |
|
21 |
20
|
rgenw |
|
22 |
|
iunss |
|
23 |
21 22
|
mpbir |
|
24 |
|
mapss |
|
25 |
9 23 24
|
mp2an |
|
26 |
11 25
|
sstri |
|
27 |
10
|
rgenw |
|
28 |
|
ixpexg |
|
29 |
27 28
|
ax-mp |
|
30 |
|
elpwg |
|
31 |
29 30
|
ax-mp |
|
32 |
26 31
|
mpbir |
|
33 |
32
|
a1i |
|
34 |
|
equid |
|
35 |
|
eqid |
|
36 |
|
equequ1 |
|
37 |
36
|
ifbid |
|
38 |
37
|
cbvixpv |
|
39 |
34 35 38
|
mpoeq123i |
|
40 |
39
|
mpteq2i |
|
41 |
1 40
|
eqtri |
|
42 |
41 2 3 4
|
hspval |
|
43 |
2
|
ovnf |
|
44 |
43
|
fdmd |
|
45 |
44
|
unieqd |
|
46 |
|
unipw |
|
47 |
46
|
a1i |
|
48 |
45 47
|
eqtrd |
|
49 |
48
|
pweqd |
|
50 |
42 49
|
eleq12d |
|
51 |
33 50
|
mpbird |
|
52 |
|
simpl |
|
53 |
|
simpr |
|
54 |
52 49
|
syl |
|
55 |
53 54
|
eleqtrd |
|
56 |
2
|
adantr |
|
57 |
|
inss1 |
|
58 |
57
|
a1i |
|
59 |
|
elpwi |
|
60 |
58 59
|
sstrd |
|
61 |
60
|
adantl |
|
62 |
56 61
|
ovnxrcl |
|
63 |
59
|
adantl |
|
64 |
63
|
ssdifssd |
|
65 |
56 64
|
ovnxrcl |
|
66 |
62 65
|
xaddcld |
|
67 |
|
pnfge |
|
68 |
66 67
|
syl |
|
69 |
68
|
adantr |
|
70 |
|
id |
|
71 |
70
|
eqcomd |
|
72 |
71
|
adantl |
|
73 |
69 72
|
breqtrd |
|
74 |
|
simpl |
|
75 |
56 63
|
ovncl |
|
76 |
75
|
adantr |
|
77 |
|
neqne |
|
78 |
77
|
adantl |
|
79 |
|
ge0xrre |
|
80 |
76 78 79
|
syl2anc |
|
81 |
56
|
adantr |
|
82 |
3
|
ad2antrr |
|
83 |
4
|
ad2antrr |
|
84 |
|
simpr |
|
85 |
63
|
adantr |
|
86 |
|
sseq1 |
|
87 |
86
|
rabbidv |
|
88 |
87
|
cbvmptv |
|
89 |
|
simpl |
|
90 |
89
|
coeq2d |
|
91 |
90
|
fveq1d |
|
92 |
91
|
fveq2d |
|
93 |
92
|
prodeq2dv |
|
94 |
93
|
cbvmptv |
|
95 |
|
fveq2 |
|
96 |
95
|
cbvixpv |
|
97 |
96
|
a1i |
|
98 |
|
fveq1 |
|
99 |
98
|
coeq2d |
|
100 |
99
|
fveq1d |
|
101 |
100
|
ixpeq2dv |
|
102 |
97 101
|
eqtrd |
|
103 |
102
|
adantr |
|
104 |
103
|
iuneq2dv |
|
105 |
104
|
sseq2d |
|
106 |
105
|
cbvrabv |
|
107 |
|
fveq1 |
|
108 |
107
|
coeq2d |
|
109 |
108
|
fveq1d |
|
110 |
109
|
ixpeq2dv |
|
111 |
110
|
adantr |
|
112 |
111
|
iuneq2dv |
|
113 |
|
fveq2 |
|
114 |
113
|
coeq2d |
|
115 |
114
|
fveq1d |
|
116 |
115
|
ixpeq2dv |
|
117 |
116
|
cbviunv |
|
118 |
117
|
a1i |
|
119 |
112 118
|
eqtrd |
|
120 |
119
|
sseq2d |
|
121 |
120
|
cbvrabv |
|
122 |
106 121
|
eqtri |
|
123 |
122
|
mpteq2i |
|
124 |
123
|
a1i |
|
125 |
|
id |
|
126 |
124 125
|
fveq12d |
|
127 |
126
|
eleq2d |
|
128 |
|
2fveq3 |
|
129 |
128
|
cbvprodv |
|
130 |
129
|
mpteq2i |
|
131 |
130
|
a1i |
|
132 |
|
fveq2 |
|
133 |
131 132
|
fveq12d |
|
134 |
133
|
cbvmptv |
|
135 |
134
|
a1i |
|
136 |
135
|
fveq2d |
|
137 |
|
fveq2 |
|
138 |
137
|
oveq1d |
|
139 |
136 138
|
breq12d |
|
140 |
127 139
|
anbi12d |
|
141 |
140
|
rabbidva2 |
|
142 |
141
|
mpteq2dv |
|
143 |
|
eqidd |
|
144 |
143
|
eleq2d |
|
145 |
|
oveq2 |
|
146 |
145
|
breq2d |
|
147 |
144 146
|
anbi12d |
|
148 |
147
|
rabbidva2 |
|
149 |
148
|
cbvmptv |
|
150 |
149
|
a1i |
|
151 |
142 150
|
eqtrd |
|
152 |
151
|
cbvmptv |
|
153 |
|
2fveq3 |
|
154 |
153
|
cbvmptv |
|
155 |
154
|
mpteq2i |
|
156 |
|
fveq2 |
|
157 |
156
|
fveq1d |
|
158 |
157
|
fveq2d |
|
159 |
158
|
mpteq2dv |
|
160 |
|
2fveq3 |
|
161 |
160
|
cbvmptv |
|
162 |
161
|
a1i |
|
163 |
159 162
|
eqtrd |
|
164 |
163
|
cbvmptv |
|
165 |
41 81 82 83 84 85 88 94 152 155 164
|
hspmbllem3 |
|
166 |
74 80 165
|
syl2anc |
|
167 |
73 166
|
pm2.61dan |
|
168 |
52 55 167
|
syl2anc |
|
169 |
5 6 7 51 168
|
caragenel2d |
|
170 |
2
|
dmvon |
|
171 |
170
|
eqcomd |
|
172 |
169 171
|
eleqtrd |
|