Theorem struct2grstr

Description: A graph represented as an extensible structure with vertices as base set and indexed edges is actually an extensible structure. (Contributed by AV, 23-Nov-2020)

	Ref	Expression
Hypothesis	struct2grvtx.g	|- G = { <. ( Base ` ndx ) , V >. , <. ( .ef ` ndx ) , E >. }
Assertion	struct2grstr	|- G Struct <. ( Base ` ndx ) , ( .ef ` ndx ) >.

Proof

Step	Hyp	Ref	Expression
1		struct2grvtx.g	|- G = { <. ( Base ` ndx ) , V >. , <. ( .ef ` ndx ) , E >. }
2		baseltedgf	|- ( Base ` ndx ) < ( .ef ` ndx )
3		edgfndxnn	|- ( .ef ` ndx ) e. NN
4	1 2 3	2strstr1	|- G Struct <. ( Base ` ndx ) , ( .ef ` ndx ) >.