Theorem bj-alalbial 31879

Description: Adding a second quantifier is a tranparent operation, (∀∀ case). (Contributed by BJ, 20-Oct-2019.)

Assertion

Ref	Expression
bj-alalbial	⊢ (∀𝑥∀𝑥𝜑 ↔ ∀𝑥𝜑)

Proof of Theorem bj-alalbial

Step	Hyp	Ref	Expression
1		nfa1 2015	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	19.3 2057	1 ⊢ (∀𝑥∀𝑥𝜑 ↔ ∀𝑥𝜑)

Syntax hints:   ↔ wb 195  ∀wal 1473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701

This theorem is referenced by: (None)