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		df-sca	⊢ Scalar = Slot 5
4		5nn	⊢ 5 ∈ ℕ
5		1lt5	⊢ 1 < 5
6	1 2 3 4 5	resslem	⊢ ( 𝐴 ∈ 𝑉 → 𝐹 = ( Scalar ‘ 𝐻 ) )