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		df-tset	$$⊢\mathrm{TopSet}=\mathrm{Slot}9$$
4		9nn	$$⊢9\in \mathbb{N}$$
5		1lt9	$$⊢1<9$$
6	1 2 3 4 5	resslem	$$⊢A\in V\to J=\mathrm{TopSet}\left(H\right)$$