This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
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 ) |