Definition df-nlfn 28705

Description: Define the null space of a Hilbert space functional. (Contributed by NM, 11-Feb-2006.) (New usage is discouraged.)

Assertion

Ref	Expression
df-nlfn	⊢ null = (𝑡 ∈ (ℂ ↑𝑚 ℋ) ↦ (◡𝑡 “ {0}))

Detailed syntax breakdown of Definition df-nlfn

Step	Hyp	Ref	Expression
1		cnl 27809	. 2 class null
2		vt	. . 3 setvar 𝑡
3		cc 9934	. . . 4 class ℂ
4		chil 27776	. . . 4 class ℋ
5		cmap 7857	. . . 4 class ↑𝑚
6	3, 4, 5	co 6650	. . 3 class (ℂ ↑𝑚 ℋ)
7	2	cv 1482	. . . . 5 class 𝑡
8	7	ccnv 5113	. . . 4 class ◡𝑡
9		cc0 9936	. . . . 5 class 0
10	9	csn 4177	. . . 4 class {0}
11	8, 10	cima 5117	. . 3 class (◡𝑡 “ {0})
12	2, 6, 11	cmpt 4729	. 2 class (𝑡 ∈ (ℂ ↑𝑚 ℋ) ↦ (◡𝑡 “ {0}))
13	1, 12	wceq 1483	1 wff null = (𝑡 ∈ (ℂ ↑𝑚 ℋ) ↦ (◡𝑡 “ {0}))

This definition is referenced by:  nlfnval  28740