Metamath Proof Explorer


Theorem ich2al

Description: Two setvar variables are always interchangeable when there are two universal quantifiers. (Contributed by SN, 23-Nov-2023)

Ref Expression
Assertion ich2al ⊢ x ⇄ y ∀ x ∀ y φ

Proof

Step Hyp Ref Expression
1 nfa1 ⊢ Ⅎ x ∀ x ∀ y φ
2 nfa2 ⊢ Ⅎ y ∀ x ∀ y φ
3 1 2 ichf ⊢ x ⇄ y ∀ x ∀ y φ