Theorem pjcoi

Description: Composition of projections. (Contributed by NM, 16-Aug-2000) (New usage is discouraged.)

	Ref	Expression
Hypotheses	pjco.1	|- G e. CH
	pjco.2	|- H e. CH
Assertion	pjcoi	|- ( A e. ~H -> ( ( ( projh ` G ) o. ( projh ` H ) ) ` A ) = ( ( projh ` G ) ` ( ( projh ` H ) ` A ) ) )

Proof

Step	Hyp	Ref	Expression
1		pjco.1	|- G e. CH
2		pjco.2	|- H e. CH
3	1	pjfi	|- ( projh ` G ) : ~H --> ~H
4	2	pjfi	|- ( projh ` H ) : ~H --> ~H
5	3 4	hocoi	|- ( A e. ~H -> ( ( ( projh ` G ) o. ( projh ` H ) ) ` A ) = ( ( projh ` G ) ` ( ( projh ` H ) ` A ) ) )