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	$⊢ (G \in W \land Vtx (G) = \emptyset \land iEdg (G) = \emptyset) \to G \in FriendGraph$

Proof

Step	Hyp	Ref	Expression
1		frgr0v	$⊢ (G \in W \land Vtx (G) = \emptyset) \to (G \in FriendGraph \leftrightarrow iEdg (G) = \emptyset)$
2	1	biimp3ar	$⊢ (G \in W \land Vtx (G) = \emptyset \land iEdg (G) = \emptyset) \to G \in FriendGraph$