Step |
Hyp |
Ref |
Expression |
1 |
|
diffi |
|
2 |
|
isfi |
|
3 |
|
simp3 |
|
4 |
|
en2sn |
|
5 |
4
|
3adant3 |
|
6 |
|
incom |
|
7 |
|
disjdif |
|
8 |
6 7
|
eqtri |
|
9 |
8
|
a1i |
|
10 |
|
nnord |
|
11 |
|
ordirr |
|
12 |
10 11
|
syl |
|
13 |
|
disjsn |
|
14 |
12 13
|
sylibr |
|
15 |
14
|
3ad2ant2 |
|
16 |
|
unen |
|
17 |
3 5 9 15 16
|
syl22anc |
|
18 |
|
difsnid |
|
19 |
|
df-suc |
|
20 |
19
|
eqcomi |
|
21 |
20
|
a1i |
|
22 |
18 21
|
breq12d |
|
23 |
22
|
3ad2ant1 |
|
24 |
17 23
|
mpbid |
|
25 |
|
peano2 |
|
26 |
25
|
3ad2ant2 |
|
27 |
|
cardennn |
|
28 |
24 26 27
|
syl2anc |
|
29 |
|
cardennn |
|
30 |
29
|
ancoms |
|
31 |
30
|
3adant1 |
|
32 |
|
suceq |
|
33 |
31 32
|
syl |
|
34 |
28 33
|
eqtr4d |
|
35 |
34
|
3expib |
|
36 |
35
|
com12 |
|
37 |
36
|
rexlimiva |
|
38 |
2 37
|
sylbi |
|
39 |
1 38
|
syl |
|
40 |
39
|
imp |
|