Theorem resssca

Description: Scalar is unaffected by restriction. (Contributed by Mario Carneiro, 7-Dec-2014)

	Ref	Expression
Hypotheses	resssca.1	|- H = ( G |`s A )
	resssca.2	|- F = ( Scalar ` G )
Assertion	resssca	|- ( A e. V -> F = ( Scalar ` H ) )

Proof

Step	Hyp	Ref	Expression
1		resssca.1	|- H = ( G |`s A )
2		resssca.2	|- F = ( Scalar ` G )
3		scaid	|- Scalar = Slot ( Scalar ` ndx )
4		scandxnbasendx	|- ( Scalar ` ndx ) =/= ( Base ` ndx )
5	1 2 3 4	resseqnbas	|- ( A e. V -> F = ( Scalar ` H ) )