Step |
Hyp |
Ref |
Expression |
1 |
|
satfv0.s |
|
2 |
|
peano1 |
|
3 |
|
elelsuc |
|
4 |
2 3
|
mp1i |
|
5 |
1
|
satfvsucom |
|
6 |
4 5
|
mpd3an3 |
|
7 |
|
goelel3xp |
|
8 |
|
eleq1 |
|
9 |
7 8
|
syl5ibrcom |
|
10 |
9
|
adantrd |
|
11 |
10
|
pm4.71d |
|
12 |
11
|
2rexbiia |
|
13 |
|
r19.41vv |
|
14 |
|
ancom |
|
15 |
12 13 14
|
3bitri |
|
16 |
15
|
opabbii |
|
17 |
|
omex |
|
18 |
17 17
|
xpex |
|
19 |
|
xpexg |
|
20 |
|
oveq1 |
|
21 |
20
|
eqeq2d |
|
22 |
|
fveq2 |
|
23 |
22
|
breq1d |
|
24 |
23
|
rabbidv |
|
25 |
24
|
eqeq2d |
|
26 |
21 25
|
anbi12d |
|
27 |
|
oveq2 |
|
28 |
27
|
eqeq2d |
|
29 |
|
fveq2 |
|
30 |
29
|
breq2d |
|
31 |
30
|
rabbidv |
|
32 |
31
|
eqeq2d |
|
33 |
28 32
|
anbi12d |
|
34 |
26 33
|
cbvrex2vw |
|
35 |
|
eqeq1 |
|
36 |
35
|
adantl |
|
37 |
|
goeleq12bg |
|
38 |
22
|
eqcomd |
|
39 |
29
|
eqcomd |
|
40 |
38 39
|
breqan12d |
|
41 |
40
|
rabbidv |
|
42 |
37 41
|
syl6bi |
|
43 |
42
|
imp |
|
44 |
|
eqeq12 |
|
45 |
43 44
|
syl5ibrcom |
|
46 |
45
|
exp4b |
|
47 |
46
|
adantr |
|
48 |
36 47
|
sylbid |
|
49 |
48
|
impd |
|
50 |
49
|
com23 |
|
51 |
50
|
expimpd |
|
52 |
51
|
rexlimdvva |
|
53 |
52
|
com23 |
|
54 |
53
|
rexlimivv |
|
55 |
34 54
|
sylbi |
|
56 |
55
|
imp |
|
57 |
56
|
gen2 |
|
58 |
|
eqeq1 |
|
59 |
58
|
anbi2d |
|
60 |
59
|
2rexbidv |
|
61 |
60
|
mo4 |
|
62 |
57 61
|
mpbir |
|
63 |
|
moabex |
|
64 |
62 63
|
mp1i |
|
65 |
19 64
|
opabex3d |
|
66 |
17 18 65
|
mp2an |
|
67 |
16 66
|
eqeltri |
|
68 |
67
|
rdg0 |
|
69 |
6 68
|
eqtrdi |
|