Theorem ressds

Description: dist is unaffected by restriction. (Contributed by Mario Carneiro, 26-Aug-2015)

	Ref	Expression
Hypotheses	ressds.1	|- H = ( G |`s A )
	ressds.2	|- D = ( dist ` G )
Assertion	ressds	|- ( A e. V -> D = ( dist ` H ) )

Proof

Step	Hyp	Ref	Expression
1		ressds.1	|- H = ( G |`s A )
2		ressds.2	|- D = ( dist ` G )
3		dsid	|- dist = Slot ( dist ` ndx )
4		dsndxnbasendx	|- ( dist ` ndx ) =/= ( Base ` ndx )
5	1 2 3 4	resseqnbas	|- ( A e. V -> D = ( dist ` H ) )