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Mirrors > Home > MPE Home > Th. List > ralimd6v | Structured version Visualization version GIF version |
Description: Deduction sextupally quantifying both antecedent and consequent. (Contributed by Scott Fenton, 5-Mar-2025.) |
Ref | Expression |
---|---|
ralim6dv.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
ralimd6v | ⊢ (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)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralim6dv.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | ralimdvv 3206 | . 2 ⊢ (𝜑 → (∀𝑝 ∈ 𝐸 ∀𝑞 ∈ 𝐹 𝜓 → ∀𝑝 ∈ 𝐸 ∀𝑞 ∈ 𝐹 𝜒)) |
3 | 2 | ralimd4v 3207 | 1 ⊢ (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)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wral 3061 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ral 3062 |
This theorem is referenced by: mulsproplem13 27513 mulsproplem14 27514 |
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