Step |
Hyp |
Ref |
Expression |
1 |
|
mirval.p |
|- P = ( Base ` G ) |
2 |
|
mirval.d |
|- .- = ( dist ` G ) |
3 |
|
mirval.i |
|- I = ( Itv ` G ) |
4 |
|
mirval.l |
|- L = ( LineG ` G ) |
5 |
|
mirval.s |
|- S = ( pInvG ` G ) |
6 |
|
mirval.g |
|- ( ph -> G e. TarskiG ) |
7 |
|
mirval.a |
|- ( ph -> A e. P ) |
8 |
|
mirfv.m |
|- M = ( S ` A ) |
9 |
|
mirmir.b |
|- ( ph -> B e. P ) |
10 |
1 2 3 4 5 6 7 8 9
|
mircl |
|- ( ph -> ( M ` B ) e. P ) |
11 |
1 2 3 4 5 6 7 8 9
|
mircgr |
|- ( ph -> ( A .- ( M ` B ) ) = ( A .- B ) ) |
12 |
11
|
eqcomd |
|- ( ph -> ( A .- B ) = ( A .- ( M ` B ) ) ) |
13 |
1 2 3 4 5 6 7 8 9
|
mirbtwn |
|- ( ph -> A e. ( ( M ` B ) I B ) ) |
14 |
1 2 3 6 10 7 9 13
|
tgbtwncom |
|- ( ph -> A e. ( B I ( M ` B ) ) ) |
15 |
1 2 3 4 5 6 7 8 10 9 12 14
|
ismir |
|- ( ph -> B = ( M ` ( M ` B ) ) ) |
16 |
15
|
eqcomd |
|- ( ph -> ( M ` ( M ` B ) ) = B ) |