Theorem 0lnop

Description: The identically zero function is a linear Hilbert space operator. (Contributed by NM, 7-Feb-2006) (New usage is discouraged.)

	Ref	Expression
Assertion	0lnop	⊢ 0hop ∈ LinOp

Proof

Step	Hyp	Ref	Expression
1		0hmop	⊢ 0hop ∈ HrmOp
2		hmoplin	⊢ ( 0hop ∈ HrmOp → 0hop ∈ LinOp )
3	1 2	ax-mp	⊢ 0hop ∈ LinOp