Metamath Proof Explorer


Theorem pgjsgr

Description: A Petersen graph is a simple graph. (Contributed by AV, 10-Nov-2025)

Ref Expression
Assertion pgjsgr ( 5 gPetersenGr 2 ) ∈ USGraph

Proof

Step Hyp Ref Expression
1 5eluz3 5 ∈ ( ℤ ‘ 3 )
2 pglem 2 ∈ ( 1 ..^ ( ⌈ ‘ ( 5 / 2 ) ) )
3 gpgusgra ( ( 5 ∈ ( ℤ ‘ 3 ) ∧ 2 ∈ ( 1 ..^ ( ⌈ ‘ ( 5 / 2 ) ) ) ) → ( 5 gPetersenGr 2 ) ∈ USGraph )
4 1 2 3 mp2an ( 5 gPetersenGr 2 ) ∈ USGraph