Theorem pjvi

Description: The value of a projection in terms of components. (Contributed by NM, 28-Nov-2000) (New usage is discouraged.)

	Ref	Expression
Hypothesis	pjfn.1	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	pjvi	$$⊢\left(A\in H\wedge B\in \perp \left(H\right)\right)\to {\mathrm{proj}}_{ℎ}\left(H\right)\left(A{+}_{ℎ}B\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		pjfn.1	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}$$
2	1	pjcompi	$$⊢\left(A\in H\wedge B\in \perp \left(H\right)\right)\to {\mathrm{proj}}_{ℎ}\left(H\right)\left(A{+}_{ℎ}B\right)=A$$