Step |
Hyp |
Ref |
Expression |
1 |
|
sge0xp.1 |
|
2 |
|
sge0xp.z |
|
3 |
|
sge0xp.a |
|
4 |
|
sge0xp.b |
|
5 |
|
sge0xp.d |
|
6 |
|
snex |
|
7 |
6
|
a1i |
|
8 |
7 4
|
xpexd |
|
9 |
8
|
adantr |
|
10 |
|
disjsnxp |
|
11 |
10
|
a1i |
|
12 |
|
vex |
|
13 |
|
elsnxp |
|
14 |
12 13
|
ax-mp |
|
15 |
14
|
biimpi |
|
16 |
15
|
adantl |
|
17 |
|
nfv |
|
18 |
1 17
|
nfan |
|
19 |
|
nfv |
|
20 |
18 19
|
nfan |
|
21 |
|
nfv |
|
22 |
2
|
3ad2ant3 |
|
23 |
5
|
3expa |
|
24 |
23
|
3adant3 |
|
25 |
22 24
|
eqeltrd |
|
26 |
25
|
3exp |
|
27 |
26
|
adantr |
|
28 |
20 21 27
|
rexlimd |
|
29 |
16 28
|
mpd |
|
30 |
29
|
3impa |
|
31 |
3 9 11 30
|
sge0iunmpt |
|
32 |
|
iunxpconst |
|
33 |
32
|
eqcomi |
|
34 |
33
|
a1i |
|
35 |
34
|
mpteq1d |
|
36 |
35
|
fveq2d |
|
37 |
|
nfv |
|
38 |
|
nfv |
|
39 |
4
|
adantr |
|
40 |
|
simpr |
|
41 |
|
eqid |
|
42 |
40 41
|
projf1o |
|
43 |
|
eqidd |
|
44 |
|
opeq2 |
|
45 |
44
|
adantl |
|
46 |
|
simpr |
|
47 |
|
opex |
|
48 |
47
|
a1i |
|
49 |
43 45 46 48
|
fvmptd |
|
50 |
49
|
adantlr |
|
51 |
38 18 2 39 42 50 29
|
sge0f1o |
|
52 |
51
|
eqcomd |
|
53 |
37 52
|
mpteq2da |
|
54 |
53
|
fveq2d |
|
55 |
31 36 54
|
3eqtr4rd |
|