Theorem lncnbd

Description: A continuous linear operator is a bounded linear operator. (Contributed by NM, 18-Feb-2006) (New usage is discouraged.)

	Ref	Expression
Assertion	lncnbd	$$⊢\mathrm{LinOp}\cap \mathrm{ContOp}=\mathrm{BndLinOp}$$

Proof

Step	Hyp	Ref	Expression
1		lncnopbd	$$⊢t\in \left(\mathrm{LinOp}\cap \mathrm{ContOp}\right)\leftrightarrow t\in \mathrm{BndLinOp}$$
2	1	eqriv	$$⊢\mathrm{LinOp}\cap \mathrm{ContOp}=\mathrm{BndLinOp}$$