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	$$⊢0_{\mathrm{hop}}\in \mathrm{LinOp}$$

Proof

Step	Hyp	Ref	Expression
1		0hmop	$$⊢0_{\mathrm{hop}}\in \mathrm{HrmOp}$$
2		hmoplin	$$⊢0_{\mathrm{hop}}\in \mathrm{HrmOp}\to 0_{\mathrm{hop}}\in \mathrm{LinOp}$$
3	1 2	ax-mp	$$⊢0_{\mathrm{hop}}\in \mathrm{LinOp}$$