Theorem resssca

Description: Scalar is unaffected by restriction. (Contributed by Mario Carneiro, 7-Dec-2014)

	Ref	Expression
Hypotheses	resssca.1	$$⊢H=G{\upharpoonright }_{𝑠}A$$
	resssca.2	$$⊢F=\mathrm{Scalar}\left(G\right)$$
Assertion	resssca	$$⊢A\in V\to F=\mathrm{Scalar}\left(H\right)$$

Proof

Step	Hyp	Ref	Expression
1		resssca.1	$$⊢H=G{\upharpoonright }_{𝑠}A$$
2		resssca.2	$$⊢F=\mathrm{Scalar}\left(G\right)$$
3		df-sca	$$⊢\mathrm{Scalar}=\mathrm{Slot}5$$
4		5nn	$$⊢5\in \mathbb{N}$$
5		1lt5	$$⊢1<5$$
6	1 2 3 4 5	resslem	$$⊢A\in V\to F=\mathrm{Scalar}\left(H\right)$$