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
|
cgr3simp1 |
|- ( ph -> ( A .- B ) = ( D .- E ) ) |
14 |
13
|
eqcomd |
|- ( ph -> ( D .- E ) = ( A .- B ) ) |
15 |
1 2 3 4 5 6 7 8 9 10 11 12
|
cgr3simp2 |
|- ( ph -> ( B .- C ) = ( E .- F ) ) |
16 |
15
|
eqcomd |
|- ( ph -> ( E .- F ) = ( B .- C ) ) |
17 |
1 2 3 4 5 6 7 8 9 10 11 12
|
cgr3simp3 |
|- ( ph -> ( C .- A ) = ( F .- D ) ) |
18 |
17
|
eqcomd |
|- ( ph -> ( F .- D ) = ( C .- A ) ) |
19 |
1 2 4 5 9 10 11 6 7 8 14 16 18
|
trgcgr |
|- ( ph -> <" D E F "> .~ <" A B C "> ) |