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Metamath Proof Explorer

Theorem bj-bialal

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

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

Proof

Step Hyp Ref Expression
1 nfa1 ⊢ Ⅎ x ∀ x φ
2 1 19.21 ⊢ ∀ x ∀ x φ → ψ ↔ ∀ x φ → ∀ x ψ