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 ) )