Step |
Hyp |
Ref |
Expression |
1 |
|
mthmpps.r |
|
2 |
|
mthmpps.j |
|
3 |
|
mthmpps.u |
|
4 |
|
mthmpps.d |
|
5 |
|
mthmpps.v |
|
6 |
|
mthmpps.z |
|
7 |
|
mthmpps.m |
|
8 |
|
eqid |
|
9 |
3 8
|
mthmsta |
|
10 |
|
simpr |
|
11 |
9 10
|
sseldi |
|
12 |
|
eqid |
|
13 |
4 12 8
|
elmpst |
|
14 |
11 13
|
sylib |
|
15 |
14
|
simp1d |
|
16 |
15
|
simpld |
|
17 |
|
difssd |
|
18 |
16 17
|
unssd |
|
19 |
7 18
|
eqsstrid |
|
20 |
15
|
simprd |
|
21 |
|
cnvdif |
|
22 |
|
cnvdif |
|
23 |
|
cnvxp |
|
24 |
|
cnvi |
|
25 |
23 24
|
difeq12i |
|
26 |
22 25
|
eqtri |
|
27 |
|
eqid |
|
28 |
27 4
|
mdvval |
|
29 |
28
|
cnveqi |
|
30 |
26 29 28
|
3eqtr4i |
|
31 |
|
cnvxp |
|
32 |
30 31
|
difeq12i |
|
33 |
21 32
|
eqtri |
|
34 |
33
|
a1i |
|
35 |
20 34
|
uneq12d |
|
36 |
7
|
cnveqi |
|
37 |
|
cnvun |
|
38 |
36 37
|
eqtri |
|
39 |
35 38 7
|
3eqtr4g |
|
40 |
19 39
|
jca |
|
41 |
14
|
simp2d |
|
42 |
14
|
simp3d |
|
43 |
4 12 8
|
elmpst |
|
44 |
40 41 42 43
|
syl3anbrc |
|
45 |
1 2 3
|
elmthm |
|
46 |
10 45
|
sylib |
|
47 |
|
eqid |
|
48 |
|
simpll |
|
49 |
19
|
adantr |
|
50 |
41
|
simpld |
|
51 |
50
|
adantr |
|
52 |
8 2
|
mppspst |
|
53 |
|
simprl |
|
54 |
52 53
|
sseldi |
|
55 |
8
|
mpst123 |
|
56 |
54 55
|
syl |
|
57 |
56
|
fveq2d |
|
58 |
|
simprr |
|
59 |
57 58
|
eqtr3d |
|
60 |
56 54
|
eqeltrrd |
|
61 |
|
eqid |
|
62 |
5 8 1 61
|
msrval |
|
63 |
60 62
|
syl |
|
64 |
5 8 1 6
|
msrval |
|
65 |
11 64
|
syl |
|
66 |
65
|
adantr |
|
67 |
59 63 66
|
3eqtr3d |
|
68 |
|
fvex |
|
69 |
68
|
inex1 |
|
70 |
|
fvex |
|
71 |
|
fvex |
|
72 |
69 70 71
|
otth |
|
73 |
67 72
|
sylib |
|
74 |
73
|
simp1d |
|
75 |
73
|
simp2d |
|
76 |
73
|
simp3d |
|
77 |
76
|
sneqd |
|
78 |
75 77
|
uneq12d |
|
79 |
78
|
imaeq2d |
|
80 |
79
|
unieqd |
|
81 |
80 6
|
eqtr4di |
|
82 |
81
|
sqxpeqd |
|
83 |
82
|
ineq2d |
|
84 |
74 83
|
eqtr3d |
|
85 |
|
inss1 |
|
86 |
84 85
|
eqsstrrdi |
|
87 |
|
eqidd |
|
88 |
87 75 76
|
oteq123d |
|
89 |
56 88
|
eqtrd |
|
90 |
89 54
|
eqeltrrd |
|
91 |
4 12 8
|
elmpst |
|
92 |
91
|
simp1bi |
|
93 |
92
|
simpld |
|
94 |
90 93
|
syl |
|
95 |
94
|
ssdifd |
|
96 |
|
unss12 |
|
97 |
86 95 96
|
syl2anc |
|
98 |
|
inundif |
|
99 |
98
|
eqcomi |
|
100 |
97 99 7
|
3sstr4g |
|
101 |
|
ssidd |
|
102 |
4 12 47 48 49 51 100 101
|
ss2mcls |
|
103 |
89 53
|
eqeltrrd |
|
104 |
8 2 47
|
elmpps |
|
105 |
104
|
simprbi |
|
106 |
103 105
|
syl |
|
107 |
102 106
|
sseldd |
|
108 |
46 107
|
rexlimddv |
|
109 |
8 2 47
|
elmpps |
|
110 |
44 108 109
|
sylanbrc |
|
111 |
7
|
ineq1i |
|
112 |
|
indir |
|
113 |
|
disjdifr |
|
114 |
|
0ss |
|
115 |
113 114
|
eqsstri |
|
116 |
|
ssequn2 |
|
117 |
115 116
|
mpbi |
|
118 |
111 112 117
|
3eqtri |
|
119 |
118
|
a1i |
|
120 |
119
|
oteq1d |
|
121 |
5 8 1 6
|
msrval |
|
122 |
44 121
|
syl |
|
123 |
120 122 65
|
3eqtr4d |
|
124 |
110 123
|
jca |
|
125 |
124
|
ex |
|
126 |
1 2 3
|
mthmi |
|
127 |
125 126
|
impbid1 |
|