Description: Adding a second quantifier over the same variable is a transparent operation, ( A. A. case). (Contributed by BJ, 20-Oct-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | bj-alalbial | ⊢ ( ∀ 𝑥 ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜑 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 | ⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑 | |
2 | 1 | 19.3 | ⊢ ( ∀ 𝑥 ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜑 ) |