Theorem lnop0i

Description: The value of a linear Hilbert space operator at zero is zero. Remark in Beran p. 99. (Contributed by NM, 11-May-2005) (New usage is discouraged.)

	Ref	Expression
Hypothesis	lnopl.1	|- T e. LinOp
Assertion	lnop0i	|- ( T ` 0h ) = 0h

Proof

Step	Hyp	Ref	Expression
1		lnopl.1	|- T e. LinOp
2		lnop0	|- ( T e. LinOp -> ( T ` 0h ) = 0h )
3	1 2	ax-mp	|- ( T ` 0h ) = 0h