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Definition df-2spthsot 30523
 Description: Define the collection of all simple paths of length 2 as ordered triple. (in a graph) (Contributed by Alexander van der Vekens, 1-Mar-2018.)
Assertion
Ref Expression
df-2spthsot 2SPathOnOt 2SPathOnOt
Distinct variable group:   ,,,,

Detailed syntax breakdown of Definition df-2spthsot
StepHypRef Expression
1 c2spthot 30518 . 2 2SPathOnOt
2 vv . . 3
3 ve . . 3
4 cvv 3072 . . 3
5 vt . . . . . . . 8
65cv 1369 . . . . . . 7
7 va . . . . . . . . 9
87cv 1369 . . . . . . . 8
9 vb . . . . . . . . 9
109cv 1369 . . . . . . . 8
112cv 1369 . . . . . . . . 9
123cv 1369 . . . . . . . . 9
13 c2pthonot 30519 . . . . . . . . 9 2SPathOnOt
1411, 12, 13co 6195 . . . . . . . 8 2SPathOnOt
158, 10, 14co 6195 . . . . . . 7 2SPathOnOt
166, 15wcel 1758 . . . . . 6 2SPathOnOt
1716, 9, 11wrex 2797 . . . . 5 2SPathOnOt
1817, 7, 11wrex 2797 . . . 4 2SPathOnOt
1911, 11cxp 4941 . . . . 5
2019, 11cxp 4941 . . . 4
2118, 5, 20crab 2800 . . 3 2SPathOnOt
222, 3, 4, 4, 21cmpt2 6197 . 2 2SPathOnOt
231, 22wceq 1370 1 2SPathOnOt 2SPathOnOt
 Colors of variables: wff setvar class This definition is referenced by:  2spthsot  30530
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