Theorem resvvsca

Description: .s is unaffected by scalar restriction. (Contributed by Thierry Arnoux, 6-Sep-2018)

	Ref	Expression
Hypotheses	resvbas.1	⊢ 𝐻 = ( 𝐺 ↾v 𝐴 )
	resvvsca.2	⊢ · = ( ·𝑠 ‘ 𝐺 )
Assertion	resvvsca	⊢ ( 𝐴 ∈ 𝑉 → · = ( ·𝑠 ‘ 𝐻 ) )

Proof

Step	Hyp	Ref	Expression
1		resvbas.1	⊢ 𝐻 = ( 𝐺 ↾v 𝐴 )
2		resvvsca.2	⊢ · = ( ·𝑠 ‘ 𝐺 )
3		df-vsca	⊢ ·𝑠 = Slot 6
4		6nn	⊢ 6 ∈ ℕ
5		5re	⊢ 5 ∈ ℝ
6		5lt6	⊢ 5 < 6
7	5 6	gtneii	⊢ 6 ≠ 5
8	1 2 3 4 7	resvlem	⊢ ( 𝐴 ∈ 𝑉 → · = ( ·𝑠 ‘ 𝐻 ) )