Theorem iscusgr

Description: The property of being a complete simple graph. (Contributed by AV, 1-Nov-2020)

	Ref	Expression
Assertion	iscusgr	⊢ ( 𝐺 ∈ ComplUSGraph ↔ ( 𝐺 ∈ USGraph ∧ 𝐺 ∈ ComplGraph ) )

Proof

Step	Hyp	Ref	Expression
1		df-cusgr	⊢ ComplUSGraph = ( USGraph ∩ ComplGraph )
2	1	elin2	⊢ ( 𝐺 ∈ ComplUSGraph ↔ ( 𝐺 ∈ USGraph ∧ 𝐺 ∈ ComplGraph ) )