Definition df-nlfn 29260

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 28364	. 2 class null
2		vt	. . 3 setvar 𝑡
3		cc 10250	. . . 4 class ℂ
4		chba 28331	. . . 4 class ℋ
5		cmap 8122	. . . 4 class ↑𝑚
6	3, 4, 5	co 6905	. . 3 class (ℂ ↑𝑚 ℋ)
7	2	cv 1657	. . . . 5 class 𝑡
8	7	ccnv 5341	. . . 4 class ◡𝑡
9		cc0 10252	. . . . 5 class 0
10	9	csn 4397	. . . 4 class {0}
11	8, 10	cima 5345	. . 3 class (◡𝑡 “ {0})
12	2, 6, 11	cmpt 4952	. 2 class (𝑡 ∈ (ℂ ↑𝑚 ℋ) ↦ (◡𝑡 “ {0}))
13	1, 12	wceq 1658	1 wff null = (𝑡 ∈ (ℂ ↑𝑚 ℋ) ↦ (◡𝑡 “ {0}))

This definition is referenced by:  nlfnval  29295