Metamath Proof Explorer

Theorem ralimd6vOLD

Description: Obsolete version of ralimdvv as of 18-Nov-2025. (Contributed by Scott Fenton, 2-Mar-2025) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Hypothesis ralim6dvOLD.1 ⊢ φ → ψ → χ
Assertion ralimd6vOLD ⊢ φ → ∀ x ∈ A ∀ y ∈ B ∀ z ∈ C ∀ w ∈ D ∀ p ∈ E ∀ q ∈ F ψ → ∀ x ∈ A ∀ y ∈ B ∀ z ∈ C ∀ w ∈ D ∀ p ∈ E ∀ q ∈ F χ

Proof

Step Hyp Ref Expression
1 ralim6dvOLD.1 ⊢ φ → ψ → χ
2 1 ralimdvvOLD ⊢ φ → ∀ p ∈ E ∀ q ∈ F ψ → ∀ p ∈ E ∀ q ∈ F χ
3 2 ralimd4vOLD ⊢ φ → ∀ x ∈ A ∀ y ∈ B ∀ z ∈ C ∀ w ∈ D ∀ p ∈ E ∀ q ∈ F ψ → ∀ x ∈ A ∀ y ∈ B ∀ z ∈ C ∀ w ∈ D ∀ p ∈ E ∀ q ∈ F χ