Step |
Hyp |
Ref |
Expression |
1 |
|
difexg |
|
2 |
|
enrefg |
|
3 |
1 2
|
syl |
|
4 |
3
|
3ad2ant1 |
|
5 |
|
sneq |
|
6 |
5
|
difeq2d |
|
7 |
6
|
breq2d |
|
8 |
4 7
|
syl5ibcom |
|
9 |
8
|
imp |
|
10 |
|
simpl1 |
|
11 |
|
difexg |
|
12 |
|
enrefg |
|
13 |
10 1 11 12
|
4syl |
|
14 |
|
dif32 |
|
15 |
13 14
|
breqtrdi |
|
16 |
|
simpl3 |
|
17 |
|
simpl2 |
|
18 |
|
en2sn |
|
19 |
16 17 18
|
syl2anc |
|
20 |
|
incom |
|
21 |
|
disjdif |
|
22 |
20 21
|
eqtri |
|
23 |
22
|
a1i |
|
24 |
|
incom |
|
25 |
|
disjdif |
|
26 |
24 25
|
eqtri |
|
27 |
26
|
a1i |
|
28 |
|
unen |
|
29 |
15 19 23 27 28
|
syl22anc |
|
30 |
|
simpr |
|
31 |
30
|
necomd |
|
32 |
|
eldifsn |
|
33 |
16 31 32
|
sylanbrc |
|
34 |
|
difsnid |
|
35 |
33 34
|
syl |
|
36 |
|
eldifsn |
|
37 |
17 30 36
|
sylanbrc |
|
38 |
|
difsnid |
|
39 |
37 38
|
syl |
|
40 |
29 35 39
|
3brtr3d |
|
41 |
9 40
|
pm2.61dane |
|