Theorem resstset

Description: TopSet is unaffected by restriction. (Contributed by Mario Carneiro, 13-Aug-2015)

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

Proof

Step	Hyp	Ref	Expression
1		resstset.1	$$⊢H=G{\upharpoonright }_{𝑠}A$$
2		resstset.2	$$⊢J=\mathrm{TopSet}\left(G\right)$$
3		tsetid	$$⊢\mathrm{TopSet}=\mathrm{Slot}\mathrm{TopSet}\left(\mathrm{ndx}\right)$$
4		tsetndxnbasendx	$$⊢\mathrm{TopSet}\left(\mathrm{ndx}\right)\ne {\mathrm{Base}}_{\mathrm{ndx}}$$
5	1 2 3 4	resseqnbas	$$⊢A\in V\to J=\mathrm{TopSet}\left(H\right)$$