Step |
Hyp |
Ref |
Expression |
1 |
|
xmetdcn2.1 |
|
2 |
|
xmetdcn2.2 |
|
3 |
|
xmetdcn2.3 |
|
4 |
|
xmetf |
|
5 |
|
rphalfcl |
|
6 |
|
simp-4l |
|
7 |
|
simplrl |
|
8 |
7
|
ad2antrr |
|
9 |
|
simplrr |
|
10 |
9
|
ad2antrr |
|
11 |
|
simpllr |
|
12 |
|
simplrl |
|
13 |
|
simplrr |
|
14 |
|
simprl |
|
15 |
|
simprr |
|
16 |
1 2 3 6 8 10 11 12 13 14 15
|
metdcnlem |
|
17 |
16
|
ex |
|
18 |
17
|
ralrimivva |
|
19 |
|
breq2 |
|
20 |
|
breq2 |
|
21 |
19 20
|
anbi12d |
|
22 |
21
|
imbi1d |
|
23 |
22
|
2ralbidv |
|
24 |
23
|
rspcev |
|
25 |
5 18 24
|
syl2an2 |
|
26 |
25
|
ralrimiva |
|
27 |
26
|
ralrimivva |
|
28 |
|
id |
|
29 |
2
|
xrsxmet |
|
30 |
29
|
a1i |
|
31 |
1 1 3
|
txmetcn |
|
32 |
28 30 31
|
mpd3an23 |
|
33 |
4 27 32
|
mpbir2and |
|