Theorem uhgrspan1lem1

Description: Lemma 1 for uhgrspan1 . (Contributed by AV, 19-Nov-2020)

	Ref	Expression
Hypotheses	uhgrspan1.v	|- V = ( Vtx ` G )
	uhgrspan1.i	|- I = ( iEdg ` G )
	uhgrspan1.f	|- F = { i e. dom I | N e/ ( I ` i ) }
Assertion	uhgrspan1lem1	|- ( ( V \ { N } ) e. _V /\ ( I |` F ) e. _V )

Proof

Step	Hyp	Ref	Expression
1		uhgrspan1.v	|- V = ( Vtx ` G )
2		uhgrspan1.i	|- I = ( iEdg ` G )
3		uhgrspan1.f	|- F = { i e. dom I | N e/ ( I ` i ) }
4	1	fvexi	|- V e. _V
5	4	difexi	|- ( V \ { N } ) e. _V
6	2	fvexi	|- I e. _V
7	6	resex	|- ( I |` F ) e. _V
8	5 7	pm3.2i	|- ( ( V \ { N } ) e. _V /\ ( I |` F ) e. _V )