Description: The friendship condition: any two (different) vertices in a friendship graph have a unique common neighbor. (Contributed by Alexander van der Vekens, 19-Dec-2017) (Revised by AV, 29-Mar-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | frcond1.v | |
|
frcond1.e | |
||
Assertion | frcond2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frcond1.v | |
|
2 | frcond1.e | |
|
3 | 1 2 | frcond1 | |
4 | prex | |
|
5 | prex | |
|
6 | 4 5 | prss | |
7 | 6 | bicomi | |
8 | 7 | reubii | |
9 | 3 8 | syl6ib | |