Step |
Hyp |
Ref |
Expression |
1 |
|
tgcgrxfr.p |
|- P = ( Base ` G ) |
2 |
|
tgcgrxfr.m |
|- .- = ( dist ` G ) |
3 |
|
tgcgrxfr.i |
|- I = ( Itv ` G ) |
4 |
|
tgcgrxfr.r |
|- .~ = ( cgrG ` G ) |
5 |
|
tgcgrxfr.g |
|- ( ph -> G e. TarskiG ) |
6 |
|
tgbtwnxfr.a |
|- ( ph -> A e. P ) |
7 |
|
tgbtwnxfr.b |
|- ( ph -> B e. P ) |
8 |
|
tgbtwnxfr.c |
|- ( ph -> C e. P ) |
9 |
|
tgbtwnxfr.d |
|- ( ph -> D e. P ) |
10 |
|
tgbtwnxfr.e |
|- ( ph -> E e. P ) |
11 |
|
tgbtwnxfr.f |
|- ( ph -> F e. P ) |
12 |
|
tgbtwnxfr.2 |
|- ( ph -> <" A B C "> .~ <" D E F "> ) |
13 |
1 2 3 4 5 6 7 8 9 10 11 12
|
cgr3simp3 |
|- ( ph -> ( C .- A ) = ( F .- D ) ) |
14 |
1 2 3 5 8 6 11 9 13
|
tgcgrcomlr |
|- ( ph -> ( A .- C ) = ( D .- F ) ) |
15 |
1 2 3 4 5 6 7 8 9 10 11 12
|
cgr3simp2 |
|- ( ph -> ( B .- C ) = ( E .- F ) ) |
16 |
1 2 3 5 7 8 10 11 15
|
tgcgrcomlr |
|- ( ph -> ( C .- B ) = ( F .- E ) ) |
17 |
1 2 3 4 5 6 7 8 9 10 11 12
|
cgr3simp1 |
|- ( ph -> ( A .- B ) = ( D .- E ) ) |
18 |
1 2 3 5 6 7 9 10 17
|
tgcgrcomlr |
|- ( ph -> ( B .- A ) = ( E .- D ) ) |
19 |
1 2 4 5 6 8 7 9 11 10 14 16 18
|
trgcgr |
|- ( ph -> <" A C B "> .~ <" D F E "> ) |