Step |
Hyp |
Ref |
Expression |
1 |
|
smfsuplem1.m |
|
2 |
|
smfsuplem1.z |
|
3 |
|
smfsuplem1.s |
|
4 |
|
smfsuplem1.f |
|
5 |
|
smfsuplem1.d |
|
6 |
|
smfsuplem1.g |
|
7 |
|
smfsuplem1.a |
|
8 |
|
smfsuplem1.h |
|
9 |
|
smfsuplem1.i |
|
10 |
3
|
adantr |
|
11 |
4
|
ffvelrnda |
|
12 |
|
eqid |
|
13 |
10 11 12
|
smff |
|
14 |
13
|
ffnd |
|
15 |
14
|
adantr |
|
16 |
|
ssrab2 |
|
17 |
5 16
|
eqsstri |
|
18 |
|
iinss2 |
|
19 |
17 18
|
sstrid |
|
20 |
19
|
ad2antlr |
|
21 |
|
cnvimass |
|
22 |
21
|
sseli |
|
23 |
22
|
adantl |
|
24 |
|
nfv |
|
25 |
|
uzid |
|
26 |
1 25
|
syl |
|
27 |
26 2
|
eleqtrrdi |
|
28 |
27
|
ne0d |
|
29 |
28
|
adantr |
|
30 |
13
|
adantlr |
|
31 |
18
|
adantl |
|
32 |
17
|
sseli |
|
33 |
32
|
adantr |
|
34 |
31 33
|
sseldd |
|
35 |
34
|
adantll |
|
36 |
30 35
|
ffvelrnd |
|
37 |
5
|
rabeq2i |
|
38 |
37
|
simprbi |
|
39 |
38
|
adantl |
|
40 |
24 29 36 39
|
suprclrnmpt |
|
41 |
40 6
|
fmptd |
|
42 |
41
|
fdmd |
|
43 |
42
|
ad2antrr |
|
44 |
23 43
|
eleqtrd |
|
45 |
20 44
|
sseldd |
|
46 |
|
mnfxr |
|
47 |
46
|
a1i |
|
48 |
7
|
rexrd |
|
49 |
48
|
ad2antrr |
|
50 |
36
|
an32s |
|
51 |
44 50
|
syldan |
|
52 |
51
|
rexrd |
|
53 |
51
|
mnfltd |
|
54 |
22
|
adantl |
|
55 |
41
|
ffdmd |
|
56 |
55
|
ffvelrnda |
|
57 |
54 56
|
syldan |
|
58 |
57
|
adantlr |
|
59 |
7
|
ad2antrr |
|
60 |
|
an32 |
|
61 |
60
|
biimpi |
|
62 |
24 36 39
|
suprubrnmpt |
|
63 |
61 62
|
syl |
|
64 |
6
|
a1i |
|
65 |
64 40
|
fvmpt2d |
|
66 |
65
|
adantlr |
|
67 |
63 66
|
breqtrrd |
|
68 |
44 67
|
syldan |
|
69 |
46
|
a1i |
|
70 |
48
|
adantr |
|
71 |
|
simpr |
|
72 |
41
|
ffnd |
|
73 |
|
elpreima |
|
74 |
72 73
|
syl |
|
75 |
74
|
adantr |
|
76 |
71 75
|
mpbid |
|
77 |
76
|
simprd |
|
78 |
69 70 77
|
iocleubd |
|
79 |
78
|
adantlr |
|
80 |
51 58 59 68 79
|
letrd |
|
81 |
47 49 52 53 80
|
eliocd |
|
82 |
15 45 81
|
elpreimad |
|
83 |
82
|
ssd |
|
84 |
|
inss1 |
|
85 |
9 84
|
eqsstrdi |
|
86 |
83 85
|
sstrd |
|
87 |
86
|
ralrimiva |
|
88 |
|
ssiin |
|
89 |
87 88
|
sylibr |
|
90 |
21 41
|
fssdm |
|
91 |
89 90
|
ssind |
|
92 |
|
iniin1 |
|
93 |
28 92
|
syl |
|
94 |
72
|
adantr |
|
95 |
|
simpr |
|
96 |
27
|
adantr |
|
97 |
|
fveq2 |
|
98 |
97
|
ineq1d |
|
99 |
98
|
eleq2d |
|
100 |
95 96 99
|
eliind |
|
101 |
|
elinel2 |
|
102 |
100 101
|
syl |
|
103 |
46
|
a1i |
|
104 |
48
|
adantr |
|
105 |
65 40
|
eqeltrd |
|
106 |
105
|
rexrd |
|
107 |
102 106
|
syldan |
|
108 |
101
|
adantl |
|
109 |
108 105
|
syldan |
|
110 |
109
|
mnfltd |
|
111 |
100 110
|
syldan |
|
112 |
102 65
|
syldan |
|
113 |
|
nfv |
|
114 |
|
nfcv |
|
115 |
|
nfii1 |
|
116 |
114 115
|
nfel |
|
117 |
113 116
|
nfan |
|
118 |
|
simpll |
|
119 |
|
simpr |
|
120 |
|
eliinid |
|
121 |
120
|
adantll |
|
122 |
|
elinel1 |
|
123 |
122
|
3ad2ant3 |
|
124 |
|
elinel2 |
|
125 |
124
|
adantl |
|
126 |
34
|
ancoms |
|
127 |
125 126
|
syldan |
|
128 |
127
|
3adant1 |
|
129 |
123 128
|
elind |
|
130 |
9
|
3adant3 |
|
131 |
129 130
|
eleqtrrd |
|
132 |
46
|
a1i |
|
133 |
48
|
3ad2ant1 |
|
134 |
|
simp3 |
|
135 |
|
elpreima |
|
136 |
14 135
|
syl |
|
137 |
136
|
3adant3 |
|
138 |
134 137
|
mpbid |
|
139 |
138
|
simprd |
|
140 |
132 133 139
|
iocleubd |
|
141 |
131 140
|
syld3an3 |
|
142 |
118 119 121 141
|
syl3anc |
|
143 |
142
|
ex |
|
144 |
117 143
|
ralrimi |
|
145 |
28
|
adantr |
|
146 |
102 36
|
syldanl |
|
147 |
102 38
|
syl |
|
148 |
7
|
adantr |
|
149 |
117 145 146 147 148
|
suprleubrnmpt |
|
150 |
144 149
|
mpbird |
|
151 |
112 150
|
eqbrtrd |
|
152 |
103 104 107 111 151
|
eliocd |
|
153 |
94 102 152
|
elpreimad |
|
154 |
153
|
ssd |
|
155 |
93 154
|
eqsstrd |
|
156 |
91 155
|
eqssd |
|
157 |
|
eqid |
|
158 |
|
fvex |
|
159 |
158
|
dmex |
|
160 |
159
|
rgenw |
|
161 |
160
|
a1i |
|
162 |
28 161
|
iinexd |
|
163 |
157 162
|
rabexd |
|
164 |
5 163
|
eqeltrid |
|
165 |
2
|
uzct |
|
166 |
165
|
a1i |
|
167 |
8
|
ffvelrnda |
|
168 |
3 166 28 167
|
saliincl |
|
169 |
|
eqid |
|
170 |
3 164 168 169
|
elrestd |
|
171 |
156 170
|
eqeltrd |
|