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 ∈ Cℋ
Assertion	pjvi	⊢ ( ( 𝐴 ∈ 𝐻 ∧ 𝐵 ∈ ( ⊥ ‘ 𝐻 ) ) → ( ( projℎ ‘ 𝐻 ) ‘ ( 𝐴 +ℎ 𝐵 ) ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		pjfn.1	⊢ 𝐻 ∈ Cℋ
2	1	pjcompi	⊢ ( ( 𝐴 ∈ 𝐻 ∧ 𝐵 ∈ ( ⊥ ‘ 𝐻 ) ) → ( ( projℎ ‘ 𝐻 ) ‘ ( 𝐴 +ℎ 𝐵 ) ) = 𝐴 )