Theorem pjfn

Description: Functionality of a projection. (Contributed by NM, 30-May-2006) (New usage is discouraged.)

	Ref	Expression
Assertion	pjfn	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}\to {\mathrm{proj}}_{ℎ}\left(H\right)Fn\mathscr{H}$$

Proof

Step	Hyp	Ref	Expression
1		pjhf	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}\to {\mathrm{proj}}_{ℎ}\left(H\right):\mathscr{H}⟶\mathscr{H}$$
2	1	ffnd	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}\to {\mathrm{proj}}_{ℎ}\left(H\right)Fn\mathscr{H}$$