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 e. ComplUSGraph -> G e. USGraph )

Proof

Step Hyp Ref Expression
1 iscusgr 
 |-  ( G e. ComplUSGraph <-> ( G e. USGraph /\ G e. ComplGraph ) )
2 1 simplbi 
 |-  ( G e. ComplUSGraph -> G e. USGraph )