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 ∈ 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 ∈ 𝑉 → 𝐹 = ( Scalar ‘ 𝐻 ) )