Theorem 6ralimi 3126

Description: Inference quantifying both antecedent and consequent six times, with strong hypothesis. (Contributed by Scott Fenton, 5-Mar-2025.)

Hypothesis

Ref	Expression
2ralimi.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
6ralimi	⊢ (∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 ∀𝑧 ∈ 𝐶 ∀𝑤 ∈ 𝐷 ∀𝑡 ∈ 𝐸 ∀𝑢 ∈ 𝐹 𝜑 → ∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 ∀𝑧 ∈ 𝐶 ∀𝑤 ∈ 𝐷 ∀𝑡 ∈ 𝐸 ∀𝑢 ∈ 𝐹 𝜓)

Proof of Theorem 6ralimi

Step	Hyp	Ref	Expression
1		2ralimi.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	ralimi 3082	. 2 ⊢ (∀𝑢 ∈ 𝐹 𝜑 → ∀𝑢 ∈ 𝐹 𝜓)
3	2	5ralimi 3125	1 ⊢ (∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 ∀𝑧 ∈ 𝐶 ∀𝑤 ∈ 𝐷 ∀𝑡 ∈ 𝐸 ∀𝑢 ∈ 𝐹 𝜑 → ∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 ∀𝑧 ∈ 𝐶 ∀𝑤 ∈ 𝐷 ∀𝑡 ∈ 𝐸 ∀𝑢 ∈ 𝐹 𝜓)

Syntax hints:   → wi 4  ∀wral 3060

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 206  df-ral 3061

This theorem is referenced by:  mulsproplem12  27496  mulsproplem13  27497  mulsproplem14  27498