Step |
Hyp |
Ref |
Expression |
1 |
|
tgsas.p |
|- P = ( Base ` G ) |
2 |
|
tgsas.m |
|- .- = ( dist ` G ) |
3 |
|
tgsas.i |
|- I = ( Itv ` G ) |
4 |
|
tgsas.g |
|- ( ph -> G e. TarskiG ) |
5 |
|
tgsas.a |
|- ( ph -> A e. P ) |
6 |
|
tgsas.b |
|- ( ph -> B e. P ) |
7 |
|
tgsas.c |
|- ( ph -> C e. P ) |
8 |
|
tgsas.d |
|- ( ph -> D e. P ) |
9 |
|
tgsas.e |
|- ( ph -> E e. P ) |
10 |
|
tgsas.f |
|- ( ph -> F e. P ) |
11 |
|
tgsas.1 |
|- ( ph -> ( A .- B ) = ( D .- E ) ) |
12 |
|
tgsas.2 |
|- ( ph -> <" A B C "> ( cgrA ` G ) <" D E F "> ) |
13 |
|
tgsas.3 |
|- ( ph -> ( B .- C ) = ( E .- F ) ) |
14 |
|
tgsas2.4 |
|- ( ph -> A =/= C ) |
15 |
|
eqid |
|- ( hlG ` G ) = ( hlG ` G ) |
16 |
|
eqid |
|- ( cgrG ` G ) = ( cgrG ` G ) |
17 |
1 2 3 4 5 6 7 8 9 10 11 12 13
|
tgsas |
|- ( ph -> <" A B C "> ( cgrG ` G ) <" D E F "> ) |
18 |
1 2 3 16 4 5 6 7 8 9 10 17
|
cgr3rotr |
|- ( ph -> <" C A B "> ( cgrG ` G ) <" F D E "> ) |
19 |
1 2 3 4 5 6 7 8 9 10 11 12 13
|
tgsas1 |
|- ( ph -> ( C .- A ) = ( F .- D ) ) |
20 |
14
|
necomd |
|- ( ph -> C =/= A ) |
21 |
1 2 3 4 7 5 10 8 19 20
|
tgcgrneq |
|- ( ph -> F =/= D ) |
22 |
1 3 15 10 5 8 4 21
|
hlid |
|- ( ph -> F ( ( hlG ` G ) ` D ) F ) |
23 |
1 3 15 4 5 6 7 8 9 10 12
|
cgrane3 |
|- ( ph -> E =/= D ) |
24 |
1 3 15 9 5 8 4 23
|
hlid |
|- ( ph -> E ( ( hlG ` G ) ` D ) E ) |
25 |
1 3 15 4 7 5 6 10 8 9 10 9 18 22 24
|
iscgrad |
|- ( ph -> <" C A B "> ( cgrA ` G ) <" F D E "> ) |