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Metamath Proof Explorer

Theorem bj-wnfanf

Description: When ph is substituted for ps , this statement expresses that weak nonfreeness implies the universal form of nonfreeness. (Contributed by BJ, 9-Dec-2023)

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

Proof

Step Hyp Ref Expression
1 bj-wnf1 ⊢ ∃ x φ → ∀ x ψ → ∀ x ∃ x φ → ∀ x ψ
2 bj-19.23bit ⊢ ∃ x φ → ∀ x ψ → φ → ∀ x ψ
3 1 2 sylg ⊢ ∃ x φ → ∀ x ψ → ∀ x φ → ∀ x ψ