Metamath Proof Explorer


Theorem pjclii

Description: Closure of a projection in its subspace. (Contributed by NM, 30-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypotheses pjcli.1 𝐻C
pjcli.2 𝐴 ∈ ℋ
Assertion pjclii ( ( proj𝐻 ) ‘ 𝐴 ) ∈ 𝐻

Proof

Step Hyp Ref Expression
1 pjcli.1 𝐻C
2 pjcli.2 𝐴 ∈ ℋ
3 1 pjcli ( 𝐴 ∈ ℋ → ( ( proj𝐻 ) ‘ 𝐴 ) ∈ 𝐻 )
4 2 3 ax-mp ( ( proj𝐻 ) ‘ 𝐴 ) ∈ 𝐻