Theorem opvtxov

Description: The set of vertices of a graph represented as an ordered pair of vertices and indexed edges as operation value. (Contributed by AV, 21-Sep-2020)

	Ref	Expression
Assertion	opvtxov	|- ( ( V e. X /\ E e. Y ) -> ( V Vtx E ) = V )

Proof

Step	Hyp	Ref	Expression
1		df-ov	|- ( V Vtx E ) = ( Vtx ` <. V , E >. )
2		opvtxfv	|- ( ( V e. X /\ E e. Y ) -> ( Vtx ` <. V , E >. ) = V )
3	1 2	syl5eq	|- ( ( V e. X /\ E e. Y ) -> ( V Vtx E ) = V )