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	$$⊢\forall x\forall x\phi \leftrightarrow \forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfa1	$$⊢Ⅎx\forall x\phi$$
2	1	19.3	$$⊢\forall x\forall x\phi \leftrightarrow \forall x\phi$$