Step |
Hyp |
Ref |
Expression |
1 |
|
pmapglb2.b |
|
2 |
|
pmapglb2.g |
|
3 |
|
pmapglb2.a |
|
4 |
|
pmapglb2.m |
|
5 |
|
hlop |
|
6 |
|
eqid |
|
7 |
2 6
|
glb0N |
|
8 |
7
|
fveq2d |
|
9 |
6 3 4
|
pmap1N |
|
10 |
8 9
|
eqtrd |
|
11 |
5 10
|
syl |
|
12 |
|
rexeq |
|
13 |
12
|
abbidv |
|
14 |
|
rex0 |
|
15 |
14
|
abf |
|
16 |
13 15
|
eqtrdi |
|
17 |
16
|
fveq2d |
|
18 |
17
|
fveq2d |
|
19 |
|
riin0 |
|
20 |
18 19
|
eqeq12d |
|
21 |
11 20
|
syl5ibrcom |
|
22 |
21
|
adantr |
|
23 |
1 2 4
|
pmapglbx |
|
24 |
|
nfv |
|
25 |
|
nfra1 |
|
26 |
24 25
|
nfan |
|
27 |
|
simpr |
|
28 |
|
simpll |
|
29 |
|
rspa |
|
30 |
29
|
adantll |
|
31 |
1 3 4
|
pmapssat |
|
32 |
28 30 31
|
syl2anc |
|
33 |
27 32
|
jca |
|
34 |
33
|
ex |
|
35 |
26 34
|
eximd |
|
36 |
|
n0 |
|
37 |
|
df-rex |
|
38 |
35 36 37
|
3imtr4g |
|
39 |
38
|
3impia |
|
40 |
|
iinss |
|
41 |
39 40
|
syl |
|
42 |
|
sseqin2 |
|
43 |
41 42
|
sylib |
|
44 |
23 43
|
eqtr4d |
|
45 |
44
|
3expia |
|
46 |
22 45
|
pm2.61dne |
|