Step |
Hyp |
Ref |
Expression |
1 |
|
issubmnd.b |
|
2 |
|
issubmnd.p |
|
3 |
|
issubmnd.z |
|
4 |
|
issubmnd.h |
|
5 |
|
simplr |
|
6 |
|
simprl |
|
7 |
|
simpll2 |
|
8 |
4 1
|
ressbas2 |
|
9 |
7 8
|
syl |
|
10 |
6 9
|
eleqtrd |
|
11 |
|
simprr |
|
12 |
11 9
|
eleqtrd |
|
13 |
|
eqid |
|
14 |
|
eqid |
|
15 |
13 14
|
mndcl |
|
16 |
5 10 12 15
|
syl3anc |
|
17 |
1
|
fvexi |
|
18 |
17
|
ssex |
|
19 |
18
|
3ad2ant2 |
|
20 |
4 2
|
ressplusg |
|
21 |
19 20
|
syl |
|
22 |
21
|
ad2antrr |
|
23 |
22
|
oveqd |
|
24 |
16 23 9
|
3eltr4d |
|
25 |
24
|
ralrimivva |
|
26 |
|
simpl2 |
|
27 |
26 8
|
syl |
|
28 |
21
|
adantr |
|
29 |
|
ovrspc2v |
|
30 |
29
|
ancoms |
|
31 |
30
|
3impb |
|
32 |
31
|
3adant1l |
|
33 |
|
simpl1 |
|
34 |
26
|
sseld |
|
35 |
26
|
sseld |
|
36 |
26
|
sseld |
|
37 |
34 35 36
|
3anim123d |
|
38 |
37
|
imp |
|
39 |
1 2
|
mndass |
|
40 |
33 38 39
|
syl2an2r |
|
41 |
|
simpl3 |
|
42 |
26
|
sselda |
|
43 |
1 2 3
|
mndlid |
|
44 |
33 42 43
|
syl2an2r |
|
45 |
1 2 3
|
mndrid |
|
46 |
33 42 45
|
syl2an2r |
|
47 |
27 28 32 40 41 44 46
|
ismndd |
|
48 |
25 47
|
impbida |
|