Theorem ressds

Description: dist is unaffected by restriction. (Contributed by Mario Carneiro, 26-Aug-2015)

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

Proof

Step	Hyp	Ref	Expression
1		ressds.1	$$⊢H=G{\upharpoonright }_{𝑠}A$$
2		ressds.2	$$⊢D=\mathrm{dist}\left(G\right)$$
3		dsid	$$⊢\mathrm{dist}=\mathrm{Slot}\mathrm{dist}\left(\mathrm{ndx}\right)$$
4		dsndxnbasendx	$$⊢\mathrm{dist}\left(\mathrm{ndx}\right)\ne {\mathrm{Base}}_{\mathrm{ndx}}$$
5	1 2 3 4	resseqnbas	$$⊢A\in V\to D=\mathrm{dist}\left(H\right)$$