Step |
Hyp |
Ref |
Expression |
1 |
|
simpl1 |
|
2 |
|
simpl2 |
|
3 |
|
simprl |
|
4 |
|
elicc1 |
|
5 |
4
|
biimpa |
|
6 |
5
|
simp1d |
|
7 |
1 2 3 6
|
syl21anc |
|
8 |
5
|
simp3d |
|
9 |
1 2 3 8
|
syl21anc |
|
10 |
1 2
|
jca |
|
11 |
|
simprr |
|
12 |
5
|
simp2d |
|
13 |
10 3 12
|
syl2anc |
|
14 |
|
elico1 |
|
15 |
14
|
notbid |
|
16 |
15
|
biimpa |
|
17 |
|
df-3an |
|
18 |
17
|
notbii |
|
19 |
|
imnan |
|
20 |
18 19
|
bitr4i |
|
21 |
16 20
|
sylib |
|
22 |
21
|
imp |
|
23 |
10 11 7 13 22
|
syl22anc |
|
24 |
|
xeqlelt |
|
25 |
24
|
biimpar |
|
26 |
7 2 9 23 25
|
syl22anc |
|
27 |
26
|
ex |
|
28 |
|
pm5.6 |
|
29 |
27 28
|
sylib |
|
30 |
|
icossicc |
|
31 |
|
simpr |
|
32 |
30 31
|
sselid |
|
33 |
|
simpr |
|
34 |
|
simpl2 |
|
35 |
33 34
|
eqeltrd |
|
36 |
|
simpl3 |
|
37 |
36 33
|
breqtrrd |
|
38 |
34
|
xrleidd |
|
39 |
33 38
|
eqbrtrd |
|
40 |
|
simpl1 |
|
41 |
40 34 4
|
syl2anc |
|
42 |
35 37 39 41
|
mpbir3and |
|
43 |
32 42
|
jaodan |
|
44 |
43
|
ex |
|
45 |
29 44
|
impbid |
|