Step |
Hyp |
Ref |
Expression |
1 |
|
suprnmpt.a |
|
2 |
|
suprnmpt.b |
|
3 |
|
suprnmpt.bnd |
|
4 |
|
suprnmpt.f |
|
5 |
|
suprnmpt.c |
|
6 |
2
|
ralrimiva |
|
7 |
4
|
rnmptss |
|
8 |
6 7
|
syl |
|
9 |
|
nfv |
|
10 |
|
nfmpt1 |
|
11 |
4 10
|
nfcxfr |
|
12 |
11
|
nfrn |
|
13 |
|
nfcv |
|
14 |
12 13
|
nfne |
|
15 |
|
n0 |
|
16 |
1 15
|
sylib |
|
17 |
|
simpr |
|
18 |
4
|
elrnmpt1 |
|
19 |
17 2 18
|
syl2anc |
|
20 |
19
|
ne0d |
|
21 |
9 14 16 20
|
exlimdd |
|
22 |
|
nfv |
|
23 |
|
nfre1 |
|
24 |
|
simp2 |
|
25 |
|
simpl1 |
|
26 |
|
simpl3 |
|
27 |
|
vex |
|
28 |
4
|
elrnmpt |
|
29 |
27 28
|
ax-mp |
|
30 |
29
|
biimpi |
|
31 |
30
|
adantl |
|
32 |
|
simp3 |
|
33 |
|
nfra1 |
|
34 |
|
nfre1 |
|
35 |
9 33 34
|
nf3an |
|
36 |
|
nfv |
|
37 |
|
simp3 |
|
38 |
|
rspa |
|
39 |
38
|
3adant3 |
|
40 |
37 39
|
eqbrtrd |
|
41 |
40
|
3exp |
|
42 |
41
|
3ad2ant2 |
|
43 |
35 36 42
|
rexlimd |
|
44 |
32 43
|
mpd |
|
45 |
25 26 31 44
|
syl3anc |
|
46 |
45
|
ralrimiva |
|
47 |
|
19.8a |
|
48 |
24 46 47
|
syl2anc |
|
49 |
|
df-rex |
|
50 |
48 49
|
sylibr |
|
51 |
50
|
3exp |
|
52 |
22 23 51
|
rexlimd |
|
53 |
3 52
|
mpd |
|
54 |
|
suprcl |
|
55 |
8 21 53 54
|
syl3anc |
|
56 |
5 55
|
eqeltrid |
|
57 |
8
|
adantr |
|
58 |
53
|
adantr |
|
59 |
|
suprub |
|
60 |
57 20 58 19 59
|
syl31anc |
|
61 |
60 5
|
breqtrrdi |
|
62 |
61
|
ralrimiva |
|
63 |
56 62
|
jca |
|