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 RegUSGraph 𝐾 → 𝐺 ∈ USGraph )

Proof

Step	Hyp	Ref	Expression
1		rusgrprop	⊢ ( 𝐺 RegUSGraph 𝐾 → ( 𝐺 ∈ USGraph ∧ 𝐺 RegGraph 𝐾 ) )
2	1	simpld	⊢ ( 𝐺 RegUSGraph 𝐾 → 𝐺 ∈ USGraph )