This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: A symbol within a word over an alphabet belongs to the alphabet.
(Contributed by Alexander van der Vekens, 28-Jun-2018)
|
|
Ref |
Expression |
|
Assertion |
wrdsymbcl |
⊢ ( ( 𝑊 ∈ Word 𝑉 ∧ 𝐼 ∈ ( 0 ..^ ( ♯ ‘ 𝑊 ) ) ) → ( 𝑊 ‘ 𝐼 ) ∈ 𝑉 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
wrdf |
⊢ ( 𝑊 ∈ Word 𝑉 → 𝑊 : ( 0 ..^ ( ♯ ‘ 𝑊 ) ) ⟶ 𝑉 ) |
| 2 |
1
|
ffvelcdmda |
⊢ ( ( 𝑊 ∈ Word 𝑉 ∧ 𝐼 ∈ ( 0 ..^ ( ♯ ‘ 𝑊 ) ) ) → ( 𝑊 ‘ 𝐼 ) ∈ 𝑉 ) |