Step |
Hyp |
Ref |
Expression |
1 |
|
mnuprdlem1.1 |
|
2 |
|
mnuprdlem1.3 |
|
3 |
|
mnuprdlem1.4 |
|
4 |
|
mnuprdlem1.8 |
|
5 |
|
eleq1 |
|
6 |
5
|
anbi1d |
|
7 |
6
|
rexbidv |
|
8 |
|
0ex |
|
9 |
8
|
prid1 |
|
10 |
9
|
a1i |
|
11 |
7 4 10
|
rspcdva |
|
12 |
2
|
adantr |
|
13 |
|
simprl |
|
14 |
|
simpr |
|
15 |
|
0nep0 |
|
16 |
15
|
a1i |
|
17 |
|
snnzg |
|
18 |
3 17
|
syl |
|
19 |
18
|
necomd |
|
20 |
16 19
|
nelprd |
|
21 |
20
|
adantr |
|
22 |
14 21
|
elnelneqd |
|
23 |
22
|
adantrr |
|
24 |
23
|
adantrl |
|
25 |
|
elpri |
|
26 |
25 1
|
eleq2s |
|
27 |
26
|
orcomd |
|
28 |
27
|
ord |
|
29 |
13 24 28
|
sylc |
|
30 |
29
|
unieqd |
|
31 |
|
snex |
|
32 |
8 31
|
unipr |
|
33 |
|
uncom |
|
34 |
|
un0 |
|
35 |
32 33 34
|
3eqtri |
|
36 |
30 35
|
eqtrdi |
|
37 |
|
simprrr |
|
38 |
36 37
|
eqsstrrd |
|
39 |
|
snssg |
|
40 |
39
|
biimprd |
|
41 |
12 38 40
|
sylc |
|
42 |
|
eleq2w |
|
43 |
|
unieq |
|
44 |
43
|
sseq1d |
|
45 |
42 44
|
anbi12d |
|
46 |
11 41 45
|
rexlimddvcbvw |
|