Theorem cusgrcplgr

Description: A complete simple graph is a complete graph. (Contributed by AV, 1-Nov-2020)

	Ref	Expression
Assertion	cusgrcplgr	$$⊢G\in \mathrm{ComplUSGraph}\to G\in \mathrm{ComplGraph}$$

Proof

Step	Hyp	Ref	Expression
1		iscusgr	$$⊢G\in \mathrm{ComplUSGraph}\leftrightarrow \left(G\in \mathrm{USGraph}\wedge G\in \mathrm{ComplGraph}\right)$$
2	1	simprbi	$$⊢G\in \mathrm{ComplUSGraph}\to G\in \mathrm{ComplGraph}$$