Step |
Hyp |
Ref |
Expression |
1 |
|
equivcau.1 |
|
2 |
|
equivcau.2 |
|
3 |
|
equivcau.3 |
|
4 |
|
equivcau.4 |
|
5 |
|
simpr |
|
6 |
3
|
ad2antrr |
|
7 |
5 6
|
rpdivcld |
|
8 |
|
oveq2 |
|
9 |
8
|
feq3d |
|
10 |
9
|
rexbidv |
|
11 |
10
|
rspcv |
|
12 |
7 11
|
syl |
|
13 |
|
simprr |
|
14 |
|
elpmi |
|
15 |
14
|
simpld |
|
16 |
15
|
ad3antlr |
|
17 |
|
resss |
|
18 |
|
dmss |
|
19 |
17 18
|
ax-mp |
|
20 |
|
uzid |
|
21 |
20
|
ad2antrl |
|
22 |
|
fdm |
|
23 |
22
|
ad2antll |
|
24 |
21 23
|
eleqtrrd |
|
25 |
19 24
|
sseldi |
|
26 |
16 25
|
ffvelrnd |
|
27 |
|
eqid |
|
28 |
|
eqid |
|
29 |
27 28 1 2 3 4
|
metss2lem |
|
30 |
29
|
expr |
|
31 |
30
|
ralrimiva |
|
32 |
31
|
ad3antrrr |
|
33 |
|
simplr |
|
34 |
|
oveq1 |
|
35 |
|
oveq1 |
|
36 |
34 35
|
sseq12d |
|
37 |
36
|
imbi2d |
|
38 |
37
|
rspcv |
|
39 |
26 32 33 38
|
syl3c |
|
40 |
13 39
|
fssd |
|
41 |
40
|
expr |
|
42 |
41
|
reximdva |
|
43 |
12 42
|
syld |
|
44 |
43
|
ralrimdva |
|
45 |
44
|
ss2rabdv |
|
46 |
|
metxmet |
|
47 |
|
caufval |
|
48 |
2 46 47
|
3syl |
|
49 |
|
metxmet |
|
50 |
|
caufval |
|
51 |
1 49 50
|
3syl |
|
52 |
45 48 51
|
3sstr4d |
|