Step |
Hyp |
Ref |
Expression |
1 |
|
ttgval.n |
|- G = ( toTG ` H ) |
2 |
|
ttgbas.1 |
|- B = ( Base ` H ) |
3 |
|
baseid |
|- Base = Slot ( Base ` ndx ) |
4 |
|
slotslnbpsd |
|- ( ( ( LineG ` ndx ) =/= ( Base ` ndx ) /\ ( LineG ` ndx ) =/= ( +g ` ndx ) ) /\ ( ( LineG ` ndx ) =/= ( .s ` ndx ) /\ ( LineG ` ndx ) =/= ( dist ` ndx ) ) ) |
5 |
|
simpll |
|- ( ( ( ( LineG ` ndx ) =/= ( Base ` ndx ) /\ ( LineG ` ndx ) =/= ( +g ` ndx ) ) /\ ( ( LineG ` ndx ) =/= ( .s ` ndx ) /\ ( LineG ` ndx ) =/= ( dist ` ndx ) ) ) -> ( LineG ` ndx ) =/= ( Base ` ndx ) ) |
6 |
4 5
|
ax-mp |
|- ( LineG ` ndx ) =/= ( Base ` ndx ) |
7 |
6
|
necomi |
|- ( Base ` ndx ) =/= ( LineG ` ndx ) |
8 |
|
slotsinbpsd |
|- ( ( ( Itv ` ndx ) =/= ( Base ` ndx ) /\ ( Itv ` ndx ) =/= ( +g ` ndx ) ) /\ ( ( Itv ` ndx ) =/= ( .s ` ndx ) /\ ( Itv ` ndx ) =/= ( dist ` ndx ) ) ) |
9 |
|
simpll |
|- ( ( ( ( Itv ` ndx ) =/= ( Base ` ndx ) /\ ( Itv ` ndx ) =/= ( +g ` ndx ) ) /\ ( ( Itv ` ndx ) =/= ( .s ` ndx ) /\ ( Itv ` ndx ) =/= ( dist ` ndx ) ) ) -> ( Itv ` ndx ) =/= ( Base ` ndx ) ) |
10 |
8 9
|
ax-mp |
|- ( Itv ` ndx ) =/= ( Base ` ndx ) |
11 |
10
|
necomi |
|- ( Base ` ndx ) =/= ( Itv ` ndx ) |
12 |
1 3 7 11
|
ttglem |
|- ( Base ` H ) = ( Base ` G ) |
13 |
2 12
|
eqtri |
|- B = ( Base ` G ) |