Step |
Hyp |
Ref |
Expression |
1 |
|
mnuprdlem2.1 |
|
2 |
|
mnuprdlem2.4 |
|
3 |
|
mnuprdlem2.5 |
|
4 |
|
mnuprdlem2.8 |
|
5 |
|
eleq1 |
|
6 |
5
|
anbi1d |
|
7 |
6
|
rexbidv |
|
8 |
|
p0ex |
|
9 |
8
|
prid2 |
|
10 |
9
|
a1i |
|
11 |
7 4 10
|
rspcdva |
|
12 |
|
simpl |
|
13 |
|
simprl |
|
14 |
|
simpr |
|
15 |
|
0nep0 |
|
16 |
15
|
necomi |
|
17 |
16
|
a1i |
|
18 |
|
0ex |
|
19 |
18
|
sneqr |
|
20 |
19
|
eqcomd |
|
21 |
3 20
|
nsyl |
|
22 |
21
|
neqned |
|
23 |
17 22
|
nelprd |
|
24 |
23
|
adantr |
|
25 |
14 24
|
elnelneqd |
|
26 |
25
|
adantrr |
|
27 |
26
|
adantrl |
|
28 |
|
elpri |
|
29 |
28 1
|
eleq2s |
|
30 |
29
|
ord |
|
31 |
13 27 30
|
sylc |
|
32 |
31
|
unieqd |
|
33 |
|
snex |
|
34 |
8 33
|
unipr |
|
35 |
|
df-pr |
|
36 |
34 35
|
eqtr4i |
|
37 |
32 36
|
eqtrdi |
|
38 |
|
simprrr |
|
39 |
37 38
|
eqsstrrd |
|
40 |
|
prssg |
|
41 |
18 2 40
|
sylancr |
|
42 |
41
|
biimprd |
|
43 |
12 39 42
|
sylc |
|
44 |
43
|
simprd |
|
45 |
|
eleq2w |
|
46 |
|
unieq |
|
47 |
46
|
sseq1d |
|
48 |
45 47
|
anbi12d |
|
49 |
11 44 48
|
rexlimddvcbvw |
|