Metamath Proof Explorer


Theorem nfexa2

Description: An inner universal quantifier's variable is bound. (Contributed by SN, 11-Feb-2026)

Ref Expression
Assertion nfexa2 ⊢ Ⅎ x ∃ y ∀ x φ

Proof

Step Hyp Ref Expression
1 hbe1a ⊢ ∃ x ∀ x φ → ∀ x φ
2 1 nfexhe ⊢ Ⅎ x ∃ y ∀ x φ