Step |
Hyp |
Ref |
Expression |
1 |
|
ovolval4lem2.a |
|
2 |
|
ovolval4lem2.m |
|
3 |
|
ovolval4lem2.g |
|
4 |
|
iftrue |
|
5 |
4
|
opeq2d |
|
6 |
5
|
adantl |
|
7 |
|
df-br |
|
8 |
7
|
biimpi |
|
9 |
8
|
adantl |
|
10 |
6 9
|
eqeltrd |
|
11 |
|
iffalse |
|
12 |
11
|
opeq2d |
|
13 |
12
|
adantl |
|
14 |
|
elmapi |
|
15 |
14
|
ffvelrnda |
|
16 |
|
xp1st |
|
17 |
15 16
|
syl |
|
18 |
17
|
leidd |
|
19 |
|
df-br |
|
20 |
18 19
|
sylib |
|
21 |
20
|
adantr |
|
22 |
13 21
|
eqeltrd |
|
23 |
10 22
|
pm2.61dan |
|
24 |
|
xp2nd |
|
25 |
15 24
|
syl |
|
26 |
25 17
|
ifcld |
|
27 |
|
opelxpi |
|
28 |
17 26 27
|
syl2anc |
|
29 |
23 28
|
elind |
|
30 |
29 3
|
fmptd |
|
31 |
|
reex |
|
32 |
31 31
|
xpex |
|
33 |
32
|
inex2 |
|
34 |
33
|
a1i |
|
35 |
|
nnex |
|
36 |
35
|
a1i |
|
37 |
34 36
|
elmapd |
|
38 |
30 37
|
mpbird |
|
39 |
38
|
adantr |
|
40 |
|
simpr |
|
41 |
|
rexpssxrxp |
|
42 |
41
|
a1i |
|
43 |
14 42
|
fssd |
|
44 |
|
2fveq3 |
|
45 |
|
2fveq3 |
|
46 |
44 45
|
breq12d |
|
47 |
46
|
cbvrabv |
|
48 |
43 3 47
|
ovolval4lem1 |
|
49 |
48
|
simpld |
|
50 |
49
|
adantr |
|
51 |
40 50
|
sseqtrd |
|
52 |
51
|
adantrr |
|
53 |
|
simpr |
|
54 |
48
|
simprd |
|
55 |
|
coass |
|
56 |
55
|
a1i |
|
57 |
|
coass |
|
58 |
57
|
a1i |
|
59 |
54 56 58
|
3eqtr4d |
|
60 |
59
|
fveq2d |
|
61 |
60
|
adantr |
|
62 |
53 61
|
eqtrd |
|
63 |
62
|
adantrl |
|
64 |
52 63
|
jca |
|
65 |
|
coeq2 |
|
66 |
65
|
rneqd |
|
67 |
66
|
unieqd |
|
68 |
67
|
sseq2d |
|
69 |
|
coeq2 |
|
70 |
69
|
fveq2d |
|
71 |
70
|
eqeq2d |
|
72 |
68 71
|
anbi12d |
|
73 |
72
|
rspcev |
|
74 |
39 64 73
|
syl2anc |
|
75 |
74
|
rexlimiva |
|
76 |
|
inss2 |
|
77 |
|
mapss |
|
78 |
32 76 77
|
mp2an |
|
79 |
78
|
sseli |
|
80 |
79
|
adantr |
|
81 |
|
simpr |
|
82 |
|
coeq2 |
|
83 |
82
|
rneqd |
|
84 |
83
|
unieqd |
|
85 |
84
|
sseq2d |
|
86 |
|
coeq2 |
|
87 |
86
|
fveq2d |
|
88 |
87
|
eqeq2d |
|
89 |
85 88
|
anbi12d |
|
90 |
89
|
rspcev |
|
91 |
80 81 90
|
syl2anc |
|
92 |
91
|
rexlimiva |
|
93 |
75 92
|
impbii |
|
94 |
93
|
rabbii |
|
95 |
2 94
|
eqtri |
|
96 |
1 95
|
ovolval3 |
|