Metamath Proof Explorer
Description: Universal quantification implies restricted quantification. (Contributed by NM, 20-Oct-2006)
|
|
Ref |
Expression |
|
Assertion |
alral |
⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜑 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ala1 |
⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ( 𝑥 ∈ 𝐴 → 𝜑 ) ) |
2 |
|
df-ral |
⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 ↔ ∀ 𝑥 ( 𝑥 ∈ 𝐴 → 𝜑 ) ) |
3 |
1 2
|
sylibr |
⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜑 ) |