Description: Degenerated case 1 for vertices: The set of vertices of the empty set is the empty set. (Contributed by AV, 24-Sep-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | vtxval0 | ⊢ ( Vtx ‘ ∅ ) = ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0nelxp | ⊢ ¬ ∅ ∈ ( V × V ) | |
2 | 1 | iffalsei | ⊢ if ( ∅ ∈ ( V × V ) , ( 1st ‘ ∅ ) , ( Base ‘ ∅ ) ) = ( Base ‘ ∅ ) |
3 | vtxval | ⊢ ( Vtx ‘ ∅ ) = if ( ∅ ∈ ( V × V ) , ( 1st ‘ ∅ ) , ( Base ‘ ∅ ) ) | |
4 | base0 | ⊢ ∅ = ( Base ‘ ∅ ) | |
5 | 2 3 4 | 3eqtr4i | ⊢ ( Vtx ‘ ∅ ) = ∅ |