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Metamath Proof Explorer

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