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Metamath Proof Explorer
Description: Inference quantifying both antecedent and consequent six times, with
strong hypothesis. (Contributed by Scott Fenton, 5-Mar-2025)
|
|
Ref |
Expression |
|
Hypothesis |
2ralimi.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
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
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
2ralimi.1 |
⊢ ( 𝜑 → 𝜓 ) |
| 2 |
1
|
ralimi |
⊢ ( ∀ 𝑢 ∈ 𝐹 𝜑 → ∀ 𝑢 ∈ 𝐹 𝜓 ) |
| 3 |
2
|
5ralimi |
⊢ ( ∀ 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 ) |