Theorem struct2grvtx

Description: The set of vertices of a graph represented as an extensible structure with vertices as base set and indexed edges. (Contributed by AV, 23-Sep-2020)

	Ref	Expression
Hypothesis	struct2grvtx.g	|- G = { <. ( Base ` ndx ) , V >. , <. ( .ef ` ndx ) , E >. }
Assertion	struct2grvtx	|- ( ( V e. X /\ E e. Y ) -> ( Vtx ` G ) = V )

Proof

Step	Hyp	Ref	Expression
1		struct2grvtx.g	|- G = { <. ( Base ` ndx ) , V >. , <. ( .ef ` ndx ) , E >. }
2		edgfndxnn	|- ( .ef ` ndx ) e. NN
3		basendxltedgfndx	|- ( Base ` ndx ) < ( .ef ` ndx )
4	2 3 1	structvtxval	|- ( ( V e. X /\ E e. Y ) -> ( Vtx ` G ) = V )