Step |
Hyp |
Ref |
Expression |
1 |
|
satefv |
|
2 |
|
incom |
|
3 |
|
sqxpexg |
|
4 |
|
inex1g |
|
5 |
3 4
|
syl |
|
6 |
2 5
|
eqeltrid |
|
7 |
6
|
ancli |
|
8 |
7
|
adantr |
|
9 |
|
satom |
|
10 |
8 9
|
syl |
|
11 |
10
|
fveq1d |
|
12 |
|
satfun |
|
13 |
8 12
|
syl |
|
14 |
13
|
ffund |
|
15 |
10
|
eqcomd |
|
16 |
15
|
funeqd |
|
17 |
14 16
|
mpbird |
|
18 |
|
peano1 |
|
19 |
18
|
a1i |
|
20 |
18
|
a1i |
|
21 |
|
satfdmfmla |
|
22 |
6 20 21
|
mpd3an23 |
|
23 |
22
|
eqcomd |
|
24 |
23
|
eleq2d |
|
25 |
24
|
biimpa |
|
26 |
|
eqid |
|
27 |
26
|
fviunfun |
|
28 |
17 19 25 27
|
syl3anc |
|
29 |
11 28
|
eqtrd |
|
30 |
|
simpl |
|
31 |
6
|
adantr |
|
32 |
|
simpr |
|
33 |
|
eqid |
|
34 |
33
|
satfv0fvfmla0 |
|
35 |
30 31 32 34
|
syl3anc |
|
36 |
|
elmapi |
|
37 |
|
simpl |
|
38 |
|
fmla0xp |
|
39 |
38
|
eleq2i |
|
40 |
|
elxp |
|
41 |
39 40
|
bitri |
|
42 |
|
xp1st |
|
43 |
42
|
ad2antll |
|
44 |
|
vex |
|
45 |
|
vex |
|
46 |
44 45
|
op2ndd |
|
47 |
46
|
fveq2d |
|
48 |
47
|
eleq1d |
|
49 |
48
|
adantr |
|
50 |
43 49
|
mpbird |
|
51 |
50
|
exlimivv |
|
52 |
41 51
|
sylbi |
|
53 |
52
|
ad2antll |
|
54 |
37 53
|
ffvelrnd |
|
55 |
|
xp2nd |
|
56 |
55
|
ad2antll |
|
57 |
46
|
fveq2d |
|
58 |
57
|
eleq1d |
|
59 |
58
|
adantr |
|
60 |
56 59
|
mpbird |
|
61 |
60
|
exlimivv |
|
62 |
41 61
|
sylbi |
|
63 |
62
|
ad2antll |
|
64 |
37 63
|
ffvelrnd |
|
65 |
54 64
|
jca |
|
66 |
65
|
ex |
|
67 |
36 66
|
syl |
|
68 |
67
|
impcom |
|
69 |
|
brinxp |
|
70 |
69
|
bicomd |
|
71 |
68 70
|
syl |
|
72 |
|
fvex |
|
73 |
72
|
epeli |
|
74 |
71 73
|
bitrdi |
|
75 |
74
|
rabbidva |
|
76 |
35 75
|
eqtrd |
|
77 |
29 76
|
eqtrd |
|
78 |
1 77
|
eqtrd |
|