Metamath Proof Explorer

Theorem cusgrusgr

Description: A complete simple graph is a simple graph. (Contributed by Alexander van der Vekens, 13-Oct-2017) (Revised by AV, 1-Nov-2020)

Ref Expression
Assertion cusgrusgr ⊢G∈ComplUSGraph→G∈USGraph

Proof

Step Hyp Ref Expression
1 iscusgr ⊢G∈ComplUSGraph↔G∈USGraph∧G∈ComplGraph
2 1 simplbi ⊢G∈ComplUSGraph→G∈USGraph