Step |
Hyp |
Ref |
Expression |
1 |
|
dstrvprob.1 |
|
2 |
|
dstrvprob.2 |
|
3 |
|
dstrvprob.3 |
|
4 |
1
|
adantr |
|
5 |
2
|
adantr |
|
6 |
|
simpr |
|
7 |
4 5 6
|
orvcelel |
|
8 |
|
prob01 |
|
9 |
4 7 8
|
syl2anc |
|
10 |
|
elunitrn |
|
11 |
10
|
rexrd |
|
12 |
|
elunitge0 |
|
13 |
|
elxrge0 |
|
14 |
11 12 13
|
sylanbrc |
|
15 |
9 14
|
syl |
|
16 |
3 15
|
fmpt3d |
|
17 |
|
simpr |
|
18 |
17
|
oveq2d |
|
19 |
18
|
fveq2d |
|
20 |
|
brsigarn |
|
21 |
|
elrnsiga |
|
22 |
|
0elsiga |
|
23 |
20 21 22
|
mp2b |
|
24 |
23
|
a1i |
|
25 |
1 2 24
|
orvcelel |
|
26 |
1 25
|
probvalrnd |
|
27 |
3 19 24 26
|
fvmptd |
|
28 |
1 2 24
|
orvcelval |
|
29 |
28
|
fveq2d |
|
30 |
|
ima0 |
|
31 |
30
|
fveq2i |
|
32 |
|
probnul |
|
33 |
1 32
|
syl |
|
34 |
31 33
|
syl5eq |
|
35 |
27 29 34
|
3eqtrd |
|
36 |
1 2
|
rrvvf |
|
37 |
36
|
ad2antrr |
|
38 |
37
|
ffund |
|
39 |
|
unipreima |
|
40 |
39
|
fveq2d |
|
41 |
38 40
|
syl |
|
42 |
1
|
ad2antrr |
|
43 |
|
domprobmeas |
|
44 |
42 43
|
syl |
|
45 |
|
nfv |
|
46 |
|
nfv |
|
47 |
|
nfdisj1 |
|
48 |
46 47
|
nfan |
|
49 |
45 48
|
nfan |
|
50 |
|
simplll |
|
51 |
|
simpr |
|
52 |
|
simpllr |
|
53 |
|
elelpwi |
|
54 |
51 52 53
|
syl2anc |
|
55 |
1 2
|
rrvfinvima |
|
56 |
55
|
r19.21bi |
|
57 |
50 54 56
|
syl2anc |
|
58 |
57
|
ex |
|
59 |
49 58
|
ralrimi |
|
60 |
|
simprl |
|
61 |
|
simprr |
|
62 |
|
disjpreima |
|
63 |
38 61 62
|
syl2anc |
|
64 |
|
measvuni |
|
65 |
44 59 60 63 64
|
syl112anc |
|
66 |
41 65
|
eqtrd |
|
67 |
2
|
ad2antrr |
|
68 |
3
|
ad2antrr |
|
69 |
20 21
|
mp1i |
|
70 |
|
simplr |
|
71 |
|
sigaclcu |
|
72 |
69 70 60 71
|
syl3anc |
|
73 |
42 67 68 72
|
dstrvval |
|
74 |
3 9
|
fvmpt2d |
|
75 |
50 54 74
|
syl2anc |
|
76 |
42
|
adantr |
|
77 |
67
|
adantr |
|
78 |
76 77 54
|
orvcelval |
|
79 |
78
|
fveq2d |
|
80 |
75 79
|
eqtrd |
|
81 |
80
|
ex |
|
82 |
49 81
|
ralrimi |
|
83 |
49 82
|
esumeq2d |
|
84 |
66 73 83
|
3eqtr4d |
|
85 |
84
|
ex |
|
86 |
85
|
ralrimiva |
|
87 |
|
ismeas |
|
88 |
20 21 87
|
mp2b |
|
89 |
16 35 86 88
|
syl3anbrc |
|
90 |
3
|
dmeqd |
|
91 |
15
|
ralrimiva |
|
92 |
|
dmmptg |
|
93 |
91 92
|
syl |
|
94 |
90 93
|
eqtrd |
|
95 |
94
|
fveq2d |
|
96 |
89 95
|
eleqtrrd |
|
97 |
|
measbasedom |
|
98 |
96 97
|
sylibr |
|
99 |
94
|
unieqd |
|
100 |
|
unibrsiga |
|
101 |
99 100
|
eqtrdi |
|
102 |
101
|
fveq2d |
|
103 |
|
simpr |
|
104 |
103
|
oveq2d |
|
105 |
|
baselsiga |
|
106 |
20 105
|
mp1i |
|
107 |
1 2 106
|
orvcelval |
|
108 |
107
|
adantr |
|
109 |
104 108
|
eqtrd |
|
110 |
109
|
fveq2d |
|
111 |
|
fimacnv |
|
112 |
36 111
|
syl |
|
113 |
112
|
fveq2d |
|
114 |
|
probtot |
|
115 |
1 114
|
syl |
|
116 |
113 115
|
eqtrd |
|
117 |
116
|
adantr |
|
118 |
110 117
|
eqtrd |
|
119 |
|
1red |
|
120 |
3 118 106 119
|
fvmptd |
|
121 |
102 120
|
eqtrd |
|
122 |
|
elprob |
|
123 |
98 121 122
|
sylanbrc |
|