Metamath Proof Explorer

Theorem ralimd4vOLD

Description: Obsolete version of ralimd4v as of 18-Nov-2025. (Contributed by Scott Fenton, 2-Mar-2025) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Hypothesis ralimd4vOLD.1 ⊢ φ → ψ → χ
Assertion ralimd4vOLD ⊢ φ → ∀ x ∈ A ∀ y ∈ B ∀ z ∈ C ∀ w ∈ D ψ → ∀ x ∈ A ∀ y ∈ B ∀ z ∈ C ∀ w ∈ D χ

Proof

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