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Mirrors > Home > MPE Home > Th. List > 5ralimi | Structured version Visualization version GIF version |
Description: Inference quantifying both antecedent and consequent five times, with strong hypothesis. (Contributed by Scott Fenton, 5-Mar-2025.) |
Ref | Expression |
---|---|
2ralimi.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
5ralimi | ⊢ (∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 ∀𝑧 ∈ 𝐶 ∀𝑤 ∈ 𝐷 ∀𝑡 ∈ 𝐸 𝜑 → ∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 ∀𝑧 ∈ 𝐶 ∀𝑤 ∈ 𝐷 ∀𝑡 ∈ 𝐸 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2ralimi.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | ralimi 3083 | . 2 ⊢ (∀𝑡 ∈ 𝐸 𝜑 → ∀𝑡 ∈ 𝐸 𝜓) |
3 | 2 | 4ralimi 3125 | 1 ⊢ (∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 ∀𝑧 ∈ 𝐶 ∀𝑤 ∈ 𝐷 ∀𝑡 ∈ 𝐸 𝜑 → ∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 ∀𝑧 ∈ 𝐶 ∀𝑤 ∈ 𝐷 ∀𝑡 ∈ 𝐸 𝜓) |
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 |
This theorem depends on definitions: df-bi 206 df-ral 3062 |
This theorem is referenced by: 6ralimi 3127 |
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