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	⊢ ( LinOp ∩ ContOp ) = BndLinOp

Proof

Step	Hyp	Ref	Expression
1		lncnopbd	⊢ ( 𝑡 ∈ ( LinOp ∩ ContOp ) ↔ 𝑡 ∈ BndLinOp )
2	1	eqriv	⊢ ( LinOp ∩ ContOp ) = BndLinOp