Metamath Proof Explorer


Theorem bj-biexal2

Description: When ph is substituted for ps , both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019)

Ref Expression
Assertion bj-biexal2 ⊢ ∀ x ∃ x φ → ψ ↔ ∃ x φ → ∀ x ψ

Proof

Step Hyp Ref Expression
1 nfe1 ⊢ Ⅎ x ∃ x φ
2 1 19.21 ⊢ ∀ x ∃ x φ → ψ ↔ ∃ x φ → ∀ x ψ