Theorem elpjidm

Description: A projection operator is idempotent. Part of Theorem 26.1 of Halmos p. 43. (Contributed by NM, 24-Apr-2006) (New usage is discouraged.)

	Ref	Expression
Assertion	elpjidm	|- ( T e. ran projh -> ( T o. T ) = T )

Proof

Step	Hyp	Ref	Expression
1		dfpjop	|- ( T e. ran projh <-> ( T e. HrmOp /\ ( T o. T ) = T ) )
2	1	simprbi	|- ( T e. ran projh -> ( T o. T ) = T )