Metamath Proof Explorer


Theorem pjcli

Description: Closure of a projection in its subspace. (Contributed by NM, 7-Oct-2000) (New usage is discouraged.)

Ref Expression
Hypothesis pjcl.1
|- H e. CH
Assertion pjcli
|- ( A e. ~H -> ( ( projh ` H ) ` A ) e. H )

Proof

Step Hyp Ref Expression
1 pjcl.1
 |-  H e. CH
2 axpjcl
 |-  ( ( H e. CH /\ A e. ~H ) -> ( ( projh ` H ) ` A ) e. H )
3 1 2 mpan
 |-  ( A e. ~H -> ( ( projh ` H ) ` A ) e. H )