Description: Degenerated case 2 for edges: The set of indexed edges of a singleton containing an ordered pair with equal components is the singleton containing the component. (Contributed by AV, 24-Sep-2020) (Proof shortened by AV, 15-Jul-2022) (Avoid depending on this detail.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | vtxvalsnop.b | |- B e. _V |
|
vtxvalsnop.g | |- G = { <. B , B >. } |
||
Assertion | iedgvalsnop | |- ( iEdg ` G ) = { B } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtxvalsnop.b | |- B e. _V |
|
2 | vtxvalsnop.g | |- G = { <. B , B >. } |
|
3 | 2 | fveq2i | |- ( iEdg ` G ) = ( iEdg ` { <. B , B >. } ) |
4 | 1 | snopeqopsnid | |- { <. B , B >. } = <. { B } , { B } >. |
5 | 4 | fveq2i | |- ( iEdg ` { <. B , B >. } ) = ( iEdg ` <. { B } , { B } >. ) |
6 | snex | |- { B } e. _V |
|
7 | 6 6 | opiedgfvi | |- ( iEdg ` <. { B } , { B } >. ) = { B } |
8 | 3 5 7 | 3eqtri | |- ( iEdg ` G ) = { B } |