| 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 |
|
cgr3tr.j |
|- ( ph -> J e. P ) |
| 14 |
|
cgr3tr.k |
|- ( ph -> K e. P ) |
| 15 |
|
cgr3tr.l |
|- ( ph -> L e. P ) |
| 16 |
|
cgr3tr.1 |
|- ( ph -> <" D E F "> .~ <" J K L "> ) |
| 17 |
1 2 3 4 5 6 7 8 9 10 11 12
|
cgr3simp1 |
|- ( ph -> ( A .- B ) = ( D .- E ) ) |
| 18 |
1 2 3 4 5 9 10 11 13 14 15 16
|
cgr3simp1 |
|- ( ph -> ( D .- E ) = ( J .- K ) ) |
| 19 |
17 18
|
eqtrd |
|- ( ph -> ( A .- B ) = ( J .- K ) ) |
| 20 |
1 2 3 4 5 6 7 8 9 10 11 12
|
cgr3simp2 |
|- ( ph -> ( B .- C ) = ( E .- F ) ) |
| 21 |
1 2 3 4 5 9 10 11 13 14 15 16
|
cgr3simp2 |
|- ( ph -> ( E .- F ) = ( K .- L ) ) |
| 22 |
20 21
|
eqtrd |
|- ( ph -> ( B .- C ) = ( K .- L ) ) |
| 23 |
1 2 3 4 5 6 7 8 9 10 11 12
|
cgr3simp3 |
|- ( ph -> ( C .- A ) = ( F .- D ) ) |
| 24 |
1 2 3 4 5 9 10 11 13 14 15 16
|
cgr3simp3 |
|- ( ph -> ( F .- D ) = ( L .- J ) ) |
| 25 |
23 24
|
eqtrd |
|- ( ph -> ( C .- A ) = ( L .- J ) ) |
| 26 |
1 2 4 5 6 7 8 13 14 15 19 22 25
|
trgcgr |
|- ( ph -> <" A B C "> .~ <" J K L "> ) |