Metamath Proof Explorer


Theorem bj-alalbial

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 ( ∀ 𝑥𝑥 𝜑 ↔ ∀ 𝑥 𝜑 )

Proof

Step Hyp Ref Expression
1 nfa1 𝑥𝑥 𝜑
2 1 19.3 ( ∀ 𝑥𝑥 𝜑 ↔ ∀ 𝑥 𝜑 )