Step |
Hyp |
Ref |
Expression |
1 |
|
brsuccf.1 |
|
2 |
|
brsuccf.2 |
|
3 |
|
df-succf |
|
4 |
3
|
breqi |
|
5 |
1 2
|
brco |
|
6 |
|
opex |
|
7 |
|
breq1 |
|
8 |
6 7
|
ceqsexv |
|
9 |
|
snex |
|
10 |
1 9 2
|
brcup |
|
11 |
8 10
|
bitri |
|
12 |
1
|
brtxp2 |
|
13 |
12
|
anbi1i |
|
14 |
|
3anass |
|
15 |
14
|
anbi1i |
|
16 |
|
an32 |
|
17 |
|
vex |
|
18 |
17
|
ideq |
|
19 |
|
eqcom |
|
20 |
18 19
|
bitri |
|
21 |
|
vex |
|
22 |
1 21
|
brsingle |
|
23 |
20 22
|
anbi12i |
|
24 |
23
|
anbi1i |
|
25 |
|
ancom |
|
26 |
|
df-3an |
|
27 |
24 25 26
|
3bitr4i |
|
28 |
15 16 27
|
3bitri |
|
29 |
28
|
2exbii |
|
30 |
|
19.41vv |
|
31 |
|
opeq1 |
|
32 |
31
|
eqeq2d |
|
33 |
32
|
anbi1d |
|
34 |
|
opeq2 |
|
35 |
34
|
eqeq2d |
|
36 |
35
|
anbi1d |
|
37 |
1 9 33 36
|
ceqsex2v |
|
38 |
29 30 37
|
3bitr3i |
|
39 |
13 38
|
bitri |
|
40 |
39
|
exbii |
|
41 |
|
df-suc |
|
42 |
41
|
eqeq2i |
|
43 |
11 40 42
|
3bitr4i |
|
44 |
4 5 43
|
3bitri |
|