Step |
Hyp |
Ref |
Expression |
1 |
|
xpssca.t |
|
2 |
|
xpssca.g |
|
3 |
|
xpssca.1 |
|
4 |
|
xpssca.2 |
|
5 |
|
xpsvsca.x |
|
6 |
|
xpsvsca.y |
|
7 |
|
xpsvsca.k |
|
8 |
|
xpsvsca.m |
|
9 |
|
xpsvsca.n |
|
10 |
|
xpsvsca.p |
|
11 |
|
xpsvsca.3 |
|
12 |
|
xpsvsca.4 |
|
13 |
|
xpsvsca.5 |
|
14 |
|
xpsvsca.6 |
|
15 |
|
xpsvsca.7 |
|
16 |
|
df-ov |
|
17 |
|
eqid |
|
18 |
17
|
xpsfval |
|
19 |
12 13 18
|
syl2anc |
|
20 |
16 19
|
syl5eqr |
|
21 |
12 13
|
opelxpd |
|
22 |
17
|
xpsff1o2 |
|
23 |
|
f1of |
|
24 |
22 23
|
ax-mp |
|
25 |
24
|
ffvelrni |
|
26 |
21 25
|
syl |
|
27 |
20 26
|
eqeltrrd |
|
28 |
|
eqid |
|
29 |
1 5 6 3 4 17 2 28
|
xpsval |
|
30 |
1 5 6 3 4 17 2 28
|
xpsrnbas |
|
31 |
|
f1ocnv |
|
32 |
22 31
|
mp1i |
|
33 |
|
f1ofo |
|
34 |
32 33
|
syl |
|
35 |
|
ovexd |
|
36 |
2
|
fvexi |
|
37 |
36
|
a1i |
|
38 |
|
prex |
|
39 |
38
|
a1i |
|
40 |
28 37 39
|
prdssca |
|
41 |
40
|
mptru |
|
42 |
|
eqid |
|
43 |
32
|
f1ovscpbl |
|
44 |
29 30 34 35 41 7 42 10 43
|
imasvscaval |
|
45 |
11 27 44
|
mpd3an23 |
|
46 |
|
f1ocnvfv |
|
47 |
22 21 46
|
sylancr |
|
48 |
20 47
|
mpd |
|
49 |
48
|
oveq2d |
|
50 |
|
iftrue |
|
51 |
50
|
fveq2d |
|
52 |
51 8
|
eqtr4di |
|
53 |
|
eqidd |
|
54 |
|
iftrue |
|
55 |
52 53 54
|
oveq123d |
|
56 |
|
iftrue |
|
57 |
55 56
|
eqtr4d |
|
58 |
|
iffalse |
|
59 |
58
|
fveq2d |
|
60 |
59 9
|
eqtr4di |
|
61 |
|
eqidd |
|
62 |
|
iffalse |
|
63 |
60 61 62
|
oveq123d |
|
64 |
|
iffalse |
|
65 |
63 64
|
eqtr4d |
|
66 |
57 65
|
pm2.61i |
|
67 |
3
|
adantr |
|
68 |
4
|
adantr |
|
69 |
|
simpr |
|
70 |
|
fvprif |
|
71 |
67 68 69 70
|
syl3anc |
|
72 |
71
|
fveq2d |
|
73 |
|
eqidd |
|
74 |
12
|
adantr |
|
75 |
13
|
adantr |
|
76 |
|
fvprif |
|
77 |
74 75 69 76
|
syl3anc |
|
78 |
72 73 77
|
oveq123d |
|
79 |
14
|
adantr |
|
80 |
15
|
adantr |
|
81 |
|
fvprif |
|
82 |
79 80 69 81
|
syl3anc |
|
83 |
66 78 82
|
3eqtr4a |
|
84 |
83
|
mpteq2dva |
|
85 |
|
eqid |
|
86 |
36
|
a1i |
|
87 |
|
2on |
|
88 |
87
|
a1i |
|
89 |
|
fnpr2o |
|
90 |
3 4 89
|
syl2anc |
|
91 |
27 30
|
eleqtrd |
|
92 |
28 85 42 7 86 88 90 11 91
|
prdsvscaval |
|
93 |
|
fnpr2o |
|
94 |
14 15 93
|
syl2anc |
|
95 |
|
dffn5 |
|
96 |
94 95
|
sylib |
|
97 |
84 92 96
|
3eqtr4d |
|
98 |
97
|
fveq2d |
|
99 |
|
df-ov |
|
100 |
17
|
xpsfval |
|
101 |
14 15 100
|
syl2anc |
|
102 |
99 101
|
syl5eqr |
|
103 |
14 15
|
opelxpd |
|
104 |
|
f1ocnvfv |
|
105 |
22 103 104
|
sylancr |
|
106 |
102 105
|
mpd |
|
107 |
98 106
|
eqtrd |
|
108 |
45 49 107
|
3eqtr3d |
|