Description: The setvar x is not free in A. x e. A ph . (Contributed by NM, 18-Oct-1996) (Proof shortened by Wolf Lammen, 7-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | hbra1 | ⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 → ∀ 𝑥 ∀ 𝑥 ∈ 𝐴 𝜑 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 | ⊢ Ⅎ 𝑥 ∀ 𝑥 ∈ 𝐴 𝜑 | |
2 | 1 | nf5ri | ⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 → ∀ 𝑥 ∀ 𝑥 ∈ 𝐴 𝜑 ) |