Theorem rusgrusgr

Description: A k-regular simple graph is a simple graph. (Contributed by Alexander van der Vekens, 8-Jul-2018) (Revised by AV, 18-Dec-2020)

	Ref	Expression
Assertion	rusgrusgr	$$⊢G\mathrm{RegUSGraph}K\to G\in \mathrm{USGraph}$$

Proof

Step	Hyp	Ref	Expression
1		rusgrprop	$$⊢G\mathrm{RegUSGraph}K\to \left(G\in \mathrm{USGraph}\wedge G\mathrm{RegGraph}K\right)$$
2	1	simpld	$$⊢G\mathrm{RegUSGraph}K\to G\in \mathrm{USGraph}$$