Metamath Proof Explorer

Theorem frgr0vb

Description: Any null graph (without vertices and edges) is a friendship graph. (Contributed by Alexander van der Vekens, 30-Sep-2017) (Revised by AV, 29-Mar-2021)

Ref Expression
Assertion frgr0vb ⊢ G ∈ W ∧ Vtx ⁡ G = ∅ ∧ iEdg ⁡ G = ∅ → G ∈ FriendGraph

Proof

Step Hyp Ref Expression
1 frgr0v ⊢ G ∈ W ∧ Vtx ⁡ G = ∅ → G ∈ FriendGraph ↔ iEdg ⁡ G = ∅
2 1 biimp3ar ⊢ G ∈ W ∧ Vtx ⁡ G = ∅ ∧ iEdg ⁡ G = ∅ → G ∈ FriendGraph