Theorem resstset

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

	Ref	Expression
Hypotheses	resstset.1	⊢ 𝐻 = ( 𝐺 ↾s 𝐴 )
	resstset.2	⊢ 𝐽 = ( TopSet ‘ 𝐺 )
Assertion	resstset	⊢ ( 𝐴 ∈ 𝑉 → 𝐽 = ( TopSet ‘ 𝐻 ) )

Proof

Step	Hyp	Ref	Expression
1		resstset.1	⊢ 𝐻 = ( 𝐺 ↾s 𝐴 )
2		resstset.2	⊢ 𝐽 = ( TopSet ‘ 𝐺 )
3		df-tset	⊢ TopSet = Slot 9
4		9nn	⊢ 9 ∈ ℕ
5		1lt9	⊢ 1 < 9
6	1 2 3 4 5	resslem	⊢ ( 𝐴 ∈ 𝑉 → 𝐽 = ( TopSet ‘ 𝐻 ) )