Theorem 0leop

Description: The zero operator is a positive operator. (The literature calls it "positive", even though in some sense it is really "nonnegative".) Part of Example 12.2(i) in Young p. 142. (Contributed by NM, 23-Jul-2006) (New usage is discouraged.)

	Ref	Expression
Assertion	0leop	$$⊢0_{\mathrm{hop}}{\le }_{\mathrm{op}}{0}_{\mathrm{hop}}$$

Proof

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