This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem resvvsca

Description: .s is unaffected by scalar restriction. (Contributed by Thierry Arnoux, 6-Sep-2018) (Proof shortened by AV, 31-Oct-2024)

Ref Expression
Hypotheses resvbas.1 ⊢ H = G ↾ 𝑣 A
resvvsca.2 ⊢ · ˙ = ⋅ G
Assertion resvvsca ⊢ A ∈ V → · ˙ = ⋅ H

Proof

Step Hyp Ref Expression
1 resvbas.1 ⊢ H = G ↾ 𝑣 A
2 resvvsca.2 ⊢ · ˙ = ⋅ G
3 vscaid ⊢ ⋅ 𝑠 = Slot ⋅ ndx
4 vscandxnscandx ⊢ ⋅ ndx ≠ Scalar ⁡ ndx
5 1 2 3 4 resvlem ⊢ A ∈ V → · ˙ = ⋅ H