Step |
Hyp |
Ref |
Expression |
1 |
|
mclspps.d |
|
2 |
|
mclspps.e |
|
3 |
|
mclspps.c |
|
4 |
|
mclspps.1 |
|
5 |
|
mclspps.2 |
|
6 |
|
mclspps.3 |
|
7 |
|
mclspps.j |
|
8 |
|
mclspps.l |
|
9 |
|
mclspps.v |
|
10 |
|
mclspps.h |
|
11 |
|
mclspps.w |
|
12 |
|
mclspps.4 |
|
13 |
|
mclspps.5 |
|
14 |
|
mclspps.6 |
|
15 |
|
mclspps.7 |
|
16 |
|
mclspps.8 |
|
17 |
|
mclsppslem.9 |
|
18 |
|
mclsppslem.10 |
|
19 |
|
mclsppslem.11 |
|
20 |
|
mclsppslem.12 |
|
21 |
8 2
|
msubf |
|
22 |
18 21
|
syl |
|
23 |
|
eqid |
|
24 |
|
eqid |
|
25 |
23 24
|
maxsta |
|
26 |
4 25
|
syl |
|
27 |
|
eqid |
|
28 |
27 24
|
mstapst |
|
29 |
26 28
|
sstrdi |
|
30 |
29 17
|
sseldd |
|
31 |
1 2 27
|
elmpst |
|
32 |
30 31
|
sylib |
|
33 |
32
|
simp3d |
|
34 |
22 33
|
ffvelrnd |
|
35 |
|
fvco3 |
|
36 |
22 33 35
|
syl2anc |
|
37 |
8
|
msubco |
|
38 |
13 18 37
|
syl2anc |
|
39 |
8 2
|
msubf |
|
40 |
13 39
|
syl |
|
41 |
|
fco |
|
42 |
40 22 41
|
syl2anc |
|
43 |
42
|
ffnd |
|
44 |
43
|
adantr |
|
45 |
22
|
ffund |
|
46 |
31
|
simp2bi |
|
47 |
30 46
|
syl |
|
48 |
47
|
simpld |
|
49 |
9 2 10
|
mvhf |
|
50 |
|
frn |
|
51 |
4 49 50
|
3syl |
|
52 |
48 51
|
unssd |
|
53 |
22
|
fdmd |
|
54 |
52 53
|
sseqtrrd |
|
55 |
|
funimass3 |
|
56 |
45 54 55
|
syl2anc |
|
57 |
19 56
|
mpbid |
|
58 |
|
cnvco |
|
59 |
58
|
imaeq1i |
|
60 |
|
imaco |
|
61 |
59 60
|
eqtri |
|
62 |
57 61
|
sseqtrrdi |
|
63 |
62
|
unssad |
|
64 |
63
|
sselda |
|
65 |
|
elpreima |
|
66 |
65
|
simplbda |
|
67 |
44 64 66
|
syl2anc |
|
68 |
43
|
adantr |
|
69 |
62
|
unssbd |
|
70 |
69
|
adantr |
|
71 |
|
ffn |
|
72 |
4 49 71
|
3syl |
|
73 |
|
fnfvelrn |
|
74 |
72 73
|
sylan |
|
75 |
70 74
|
sseldd |
|
76 |
|
elpreima |
|
77 |
76
|
simplbda |
|
78 |
68 75 77
|
syl2anc |
|
79 |
22
|
adantr |
|
80 |
4 49
|
syl |
|
81 |
80
|
adantr |
|
82 |
32
|
simp1d |
|
83 |
82
|
simpld |
|
84 |
9 1
|
mdvval |
|
85 |
|
difss |
|
86 |
84 85
|
eqsstri |
|
87 |
83 86
|
sstrdi |
|
88 |
87
|
ssbrd |
|
89 |
88
|
imp |
|
90 |
|
brxp |
|
91 |
89 90
|
sylib |
|
92 |
91
|
simpld |
|
93 |
81 92
|
ffvelrnd |
|
94 |
|
fvco3 |
|
95 |
79 93 94
|
syl2anc |
|
96 |
95
|
fveq2d |
|
97 |
4
|
adantr |
|
98 |
13
|
adantr |
|
99 |
79 93
|
ffvelrnd |
|
100 |
8 2 11 10
|
msubvrs |
|
101 |
97 98 99 100
|
syl3anc |
|
102 |
96 101
|
eqtrd |
|
103 |
102
|
eleq2d |
|
104 |
|
eliun |
|
105 |
103 104
|
bitrdi |
|
106 |
91
|
simprd |
|
107 |
81 106
|
ffvelrnd |
|
108 |
|
fvco3 |
|
109 |
79 107 108
|
syl2anc |
|
110 |
109
|
fveq2d |
|
111 |
79 107
|
ffvelrnd |
|
112 |
8 2 11 10
|
msubvrs |
|
113 |
97 98 111 112
|
syl3anc |
|
114 |
110 113
|
eqtrd |
|
115 |
114
|
eleq2d |
|
116 |
|
eliun |
|
117 |
115 116
|
bitrdi |
|
118 |
105 117
|
anbi12d |
|
119 |
|
reeanv |
|
120 |
|
simpll |
|
121 |
|
brxp |
|
122 |
|
breq12 |
|
123 |
|
simpl |
|
124 |
123
|
fveq2d |
|
125 |
124
|
fveq2d |
|
126 |
125
|
fveq2d |
|
127 |
|
simpr |
|
128 |
127
|
fveq2d |
|
129 |
128
|
fveq2d |
|
130 |
129
|
fveq2d |
|
131 |
126 130
|
xpeq12d |
|
132 |
131
|
sseq1d |
|
133 |
122 132
|
imbi12d |
|
134 |
133
|
spc2gv |
|
135 |
134
|
el2v |
|
136 |
20 135
|
syl |
|
137 |
136
|
imp |
|
138 |
137
|
ssbrd |
|
139 |
121 138
|
syl5bir |
|
140 |
139
|
imp |
|
141 |
|
vex |
|
142 |
|
vex |
|
143 |
|
breq12 |
|
144 |
|
simpl |
|
145 |
144
|
fveq2d |
|
146 |
145
|
fveq2d |
|
147 |
146
|
fveq2d |
|
148 |
147
|
eleq2d |
|
149 |
|
simpr |
|
150 |
149
|
fveq2d |
|
151 |
150
|
fveq2d |
|
152 |
151
|
fveq2d |
|
153 |
152
|
eleq2d |
|
154 |
143 148 153
|
3anbi123d |
|
155 |
154
|
anbi2d |
|
156 |
155
|
imbi1d |
|
157 |
141 142 156 16
|
vtocl2 |
|
158 |
157
|
3exp2 |
|
159 |
158
|
imp4b |
|
160 |
120 140 159
|
syl2anc |
|
161 |
160
|
rexlimdvva |
|
162 |
119 161
|
syl5bir |
|
163 |
118 162
|
sylbid |
|
164 |
163
|
exp4b |
|
165 |
164
|
3imp2 |
|
166 |
1 2 3 4 5 6 23 8 9 10 11 17 38 67 78 165
|
mclsax |
|
167 |
36 166
|
eqeltrrd |
|
168 |
40
|
ffnd |
|
169 |
|
elpreima |
|
170 |
168 169
|
syl |
|
171 |
34 167 170
|
mpbir2and |
|