Step |
Hyp |
Ref |
Expression |
1 |
|
xpsval.t |
|
2 |
|
xpsval.x |
|
3 |
|
xpsval.y |
|
4 |
|
xpsval.1 |
|
5 |
|
xpsval.2 |
|
6 |
|
xpsadd.3 |
|
7 |
|
xpsadd.4 |
|
8 |
|
xpsadd.5 |
|
9 |
|
xpsadd.6 |
|
10 |
|
xpsadd.7 |
|
11 |
|
xpsadd.8 |
|
12 |
|
xpsaddlem.m |
|
13 |
|
xpsaddlem.n |
|
14 |
|
xpsaddlem.p |
|
15 |
|
xpsaddlem.f |
|
16 |
|
xpsaddlem.u |
|
17 |
|
xpsaddlem.1 |
|
18 |
|
xpsaddlem.2 |
|
19 |
|
df-ov |
|
20 |
15
|
xpsfval |
|
21 |
6 7 20
|
syl2anc |
|
22 |
19 21
|
syl5eqr |
|
23 |
6 7
|
opelxpd |
|
24 |
15
|
xpsff1o2 |
|
25 |
|
f1of |
|
26 |
24 25
|
ax-mp |
|
27 |
26
|
ffvelrni |
|
28 |
23 27
|
syl |
|
29 |
22 28
|
eqeltrrd |
|
30 |
|
df-ov |
|
31 |
15
|
xpsfval |
|
32 |
8 9 31
|
syl2anc |
|
33 |
30 32
|
syl5eqr |
|
34 |
8 9
|
opelxpd |
|
35 |
26
|
ffvelrni |
|
36 |
34 35
|
syl |
|
37 |
33 36
|
eqeltrrd |
|
38 |
29 37 17
|
mpd3an23 |
|
39 |
|
f1ocnvfv |
|
40 |
24 23 39
|
sylancr |
|
41 |
22 40
|
mpd |
|
42 |
|
f1ocnvfv |
|
43 |
24 34 42
|
sylancr |
|
44 |
33 43
|
mpd |
|
45 |
41 44
|
oveq12d |
|
46 |
|
iftrue |
|
47 |
46
|
fveq2d |
|
48 |
47 12
|
eqtr4di |
|
49 |
|
iftrue |
|
50 |
|
iftrue |
|
51 |
48 49 50
|
oveq123d |
|
52 |
|
iftrue |
|
53 |
51 52
|
eqtr4d |
|
54 |
|
iffalse |
|
55 |
54
|
fveq2d |
|
56 |
55 13
|
eqtr4di |
|
57 |
|
iffalse |
|
58 |
|
iffalse |
|
59 |
56 57 58
|
oveq123d |
|
60 |
|
iffalse |
|
61 |
59 60
|
eqtr4d |
|
62 |
53 61
|
pm2.61i |
|
63 |
4
|
adantr |
|
64 |
5
|
adantr |
|
65 |
|
simpr |
|
66 |
|
fvprif |
|
67 |
63 64 65 66
|
syl3anc |
|
68 |
67
|
fveq2d |
|
69 |
6
|
adantr |
|
70 |
7
|
adantr |
|
71 |
|
fvprif |
|
72 |
69 70 65 71
|
syl3anc |
|
73 |
8
|
adantr |
|
74 |
9
|
adantr |
|
75 |
|
fvprif |
|
76 |
73 74 65 75
|
syl3anc |
|
77 |
68 72 76
|
oveq123d |
|
78 |
10
|
adantr |
|
79 |
11
|
adantr |
|
80 |
|
fvprif |
|
81 |
78 79 65 80
|
syl3anc |
|
82 |
62 77 81
|
3eqtr4a |
|
83 |
82
|
mpteq2dva |
|
84 |
|
fnpr2o |
|
85 |
4 5 84
|
syl2anc |
|
86 |
|
eqid |
|
87 |
1 2 3 4 5 15 86 16
|
xpsrnbas |
|
88 |
29 87
|
eleqtrd |
|
89 |
37 87
|
eleqtrd |
|
90 |
85 88 89 18
|
syl3anc |
|
91 |
|
fnpr2o |
|
92 |
10 11 91
|
syl2anc |
|
93 |
|
dffn5 |
|
94 |
92 93
|
sylib |
|
95 |
83 90 94
|
3eqtr4d |
|
96 |
95
|
fveq2d |
|
97 |
|
df-ov |
|
98 |
15
|
xpsfval |
|
99 |
10 11 98
|
syl2anc |
|
100 |
97 99
|
syl5eqr |
|
101 |
10 11
|
opelxpd |
|
102 |
|
f1ocnvfv |
|
103 |
24 101 102
|
sylancr |
|
104 |
100 103
|
mpd |
|
105 |
96 104
|
eqtrd |
|
106 |
38 45 105
|
3eqtr3d |
|