Theorem dsid

Description: Utility theorem: index-independent form of df-ds . (Contributed by Mario Carneiro, 23-Dec-2013)

	Ref	Expression
Assertion	dsid	⊢ dist = Slot ( dist ‘ ndx )

Proof

Step	Hyp	Ref	Expression
1		df-ds	⊢ dist = Slot ; 1 2
2		1nn0	⊢ 1 ∈ ℕ0
3		2nn	⊢ 2 ∈ ℕ
4	2 3	decnncl	⊢ ; 1 2 ∈ ℕ
5	1 4	ndxid	⊢ dist = Slot ( dist ‘ ndx )