Step |
Hyp |
Ref |
Expression |
1 |
|
ssltmul1.1 |
|
2 |
|
ssltmul1.2 |
|
3 |
|
ssltmul1.3 |
|
4 |
|
ssltmul1.4 |
|
5 |
|
eqid |
|
6 |
5
|
rnmpo |
|
7 |
|
ssltex1 |
|
8 |
1 7
|
syl |
|
9 |
|
ssltex1 |
|
10 |
2 9
|
syl |
|
11 |
5
|
mpoexg |
|
12 |
8 10 11
|
syl2anc |
|
13 |
|
rnexg |
|
14 |
12 13
|
syl |
|
15 |
6 14
|
eqeltrrid |
|
16 |
|
eqid |
|
17 |
16
|
rnmpo |
|
18 |
|
ssltex2 |
|
19 |
1 18
|
syl |
|
20 |
|
ssltex2 |
|
21 |
2 20
|
syl |
|
22 |
16
|
mpoexg |
|
23 |
19 21 22
|
syl2anc |
|
24 |
|
rnexg |
|
25 |
23 24
|
syl |
|
26 |
17 25
|
eqeltrrid |
|
27 |
15 26
|
unexd |
|
28 |
|
snex |
|
29 |
28
|
a1i |
|
30 |
|
ssltss1 |
|
31 |
1 30
|
syl |
|
32 |
31
|
adantr |
|
33 |
|
simprl |
|
34 |
32 33
|
sseldd |
|
35 |
2
|
scutcld |
|
36 |
4 35
|
eqeltrd |
|
37 |
36
|
adantr |
|
38 |
34 37
|
mulscld |
|
39 |
1
|
scutcld |
|
40 |
3 39
|
eqeltrd |
|
41 |
40
|
adantr |
|
42 |
|
ssltss1 |
|
43 |
2 42
|
syl |
|
44 |
43
|
adantr |
|
45 |
|
simprr |
|
46 |
44 45
|
sseldd |
|
47 |
41 46
|
mulscld |
|
48 |
38 47
|
addscld |
|
49 |
34 46
|
mulscld |
|
50 |
48 49
|
subscld |
|
51 |
|
eleq1 |
|
52 |
50 51
|
syl5ibrcom |
|
53 |
52
|
rexlimdvva |
|
54 |
53
|
abssdv |
|
55 |
|
ssltss2 |
|
56 |
1 55
|
syl |
|
57 |
56
|
adantr |
|
58 |
|
simprl |
|
59 |
57 58
|
sseldd |
|
60 |
36
|
adantr |
|
61 |
59 60
|
mulscld |
|
62 |
40
|
adantr |
|
63 |
|
ssltss2 |
|
64 |
2 63
|
syl |
|
65 |
64
|
adantr |
|
66 |
|
simprr |
|
67 |
65 66
|
sseldd |
|
68 |
62 67
|
mulscld |
|
69 |
61 68
|
addscld |
|
70 |
59 67
|
mulscld |
|
71 |
69 70
|
subscld |
|
72 |
|
eleq1 |
|
73 |
71 72
|
syl5ibrcom |
|
74 |
73
|
rexlimdvva |
|
75 |
74
|
abssdv |
|
76 |
54 75
|
unssd |
|
77 |
40 36
|
mulscld |
|
78 |
77
|
snssd |
|
79 |
|
elun |
|
80 |
|
vex |
|
81 |
|
eqeq1 |
|
82 |
81
|
2rexbidv |
|
83 |
80 82
|
elab |
|
84 |
|
eqeq1 |
|
85 |
84
|
2rexbidv |
|
86 |
80 85
|
elab |
|
87 |
83 86
|
orbi12i |
|
88 |
79 87
|
bitri |
|
89 |
38 47 49
|
addsubsd |
|
90 |
|
scutcut |
|
91 |
1 90
|
syl |
|
92 |
91
|
simp2d |
|
93 |
92
|
adantr |
|
94 |
|
ovex |
|
95 |
94
|
snid |
|
96 |
3 95
|
eqeltrdi |
|
97 |
96
|
adantr |
|
98 |
93 33 97
|
ssltsepcd |
|
99 |
|
scutcut |
|
100 |
2 99
|
syl |
|
101 |
100
|
simp2d |
|
102 |
101
|
adantr |
|
103 |
|
ovex |
|
104 |
103
|
snid |
|
105 |
4 104
|
eqeltrdi |
|
106 |
105
|
adantr |
|
107 |
102 45 106
|
ssltsepcd |
|
108 |
34 41 46 37 98 107
|
sltmuld |
|
109 |
38 49
|
subscld |
|
110 |
77
|
adantr |
|
111 |
109 47 110
|
sltaddsubd |
|
112 |
108 111
|
mpbird |
|
113 |
89 112
|
eqbrtrd |
|
114 |
|
breq1 |
|
115 |
113 114
|
syl5ibrcom |
|
116 |
115
|
rexlimdvva |
|
117 |
61 68 70
|
addsubsd |
|
118 |
1
|
adantr |
|
119 |
118 90
|
syl |
|
120 |
119
|
simp3d |
|
121 |
3
|
adantr |
|
122 |
121 95
|
eqeltrdi |
|
123 |
120 122 58
|
ssltsepcd |
|
124 |
2
|
adantr |
|
125 |
124 99
|
syl |
|
126 |
125
|
simp3d |
|
127 |
4
|
adantr |
|
128 |
127 104
|
eqeltrdi |
|
129 |
126 128 66
|
ssltsepcd |
|
130 |
62 59 60 67 123 129
|
sltmuld |
|
131 |
61 70
|
subscld |
|
132 |
77
|
adantr |
|
133 |
131 68 132
|
sltaddsubd |
|
134 |
61 70 132 68
|
sltsubsub2bd |
|
135 |
133 134
|
bitrd |
|
136 |
130 135
|
mpbird |
|
137 |
117 136
|
eqbrtrd |
|
138 |
|
breq1 |
|
139 |
137 138
|
syl5ibrcom |
|
140 |
139
|
rexlimdvva |
|
141 |
116 140
|
jaod |
|
142 |
88 141
|
biimtrid |
|
143 |
142
|
imp |
|
144 |
|
velsn |
|
145 |
|
breq2 |
|
146 |
144 145
|
sylbi |
|
147 |
143 146
|
syl5ibrcom |
|
148 |
147
|
3impia |
|
149 |
27 29 76 78 148
|
ssltd |
|