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 "> ) |