Theorem iscusgr

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

	Ref	Expression
Assertion	iscusgr	$$⊢G\in \mathrm{ComplUSGraph}\leftrightarrow \left(G\in \mathrm{USGraph}\wedge G\in \mathrm{ComplGraph}\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-cusgr	$$⊢\mathrm{ComplUSGraph}=\mathrm{USGraph}\cap \mathrm{ComplGraph}$$
2	1	elin2	$$⊢G\in \mathrm{ComplUSGraph}\leftrightarrow \left(G\in \mathrm{USGraph}\wedge G\in \mathrm{ComplGraph}\right)$$