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Metamath Proof Explorer

Theorem bj-nfdt0

Description: A theorem close to a closed form of nf5d and nf5dh . (Contributed by BJ, 2-May-2019)

Ref Expression
Assertion bj-nfdt0 ⊢ ∀ x φ → ψ → ∀ x ψ → ∀ x φ → Ⅎ x ψ

Proof

Step Hyp Ref Expression
1 alim ⊢ ∀ x φ → ψ → ∀ x ψ → ∀ x φ → ∀ x ψ → ∀ x ψ
2 nf5 ⊢ Ⅎ x ψ ↔ ∀ x ψ → ∀ x ψ
3 1 2 imbitrrdi ⊢ ∀ x φ → ψ → ∀ x ψ → ∀ x φ → Ⅎ x ψ