Theorem ressunif

Description: UnifSet is unaffected by restriction. (Contributed by Thierry Arnoux, 7-Dec-2017)

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

Proof

Step	Hyp	Ref	Expression
1		ressunif.1	$$⊢H=G{\upharpoonright }_{𝑠}A$$
2		ressunif.2	$$⊢U=\mathrm{UnifSet}\left(G\right)$$
3		df-unif	$$⊢\mathrm{UnifSet}=\mathrm{Slot}13$$
4		1nn0	$$⊢1\in {\mathbb{N}}_0$$
5		3nn	$$⊢3\in \mathbb{N}$$
6	4 5	decnncl	$$⊢13\in \mathbb{N}$$
7		1nn	$$⊢1\in \mathbb{N}$$
8		3nn0	$$⊢3\in {\mathbb{N}}_0$$
9		1lt10	$$⊢1<10$$
10	7 8 4 9	declti	$$⊢1<13$$
11	1 2 3 6 10	resslem	$$⊢A\in V\to U=\mathrm{UnifSet}\left(H\right)$$