Metamath Proof Explorer
Description: The setvar x is not free in A. x e. A ph . (Contributed by NM, 18-Oct-1996) (Revised by Mario Carneiro, 7-Oct-2016)
|
|
Ref |
Expression |
|
Assertion |
nfra1 |
⊢ Ⅎ 𝑥 ∀ 𝑥 ∈ 𝐴 𝜑 |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
df-ral |
⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 ↔ ∀ 𝑥 ( 𝑥 ∈ 𝐴 → 𝜑 ) ) |
2 |
|
nfa1 |
⊢ Ⅎ 𝑥 ∀ 𝑥 ( 𝑥 ∈ 𝐴 → 𝜑 ) |
3 |
1 2
|
nfxfr |
⊢ Ⅎ 𝑥 ∀ 𝑥 ∈ 𝐴 𝜑 |