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| Mirrors > Home > MPE Home > Th. List > ralimi | Structured version Visualization version GIF version | ||
| Description: Inference quantifying both antecedent and consequent, with strong hypothesis. (Contributed by NM, 4-Mar-1997.) |
| Ref | Expression |
|---|---|
| ralimi.1 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| ralimi | ⊢ (∀𝑥 ∈ 𝐴 𝜑 → ∀𝑥 ∈ 𝐴 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ralimi.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 → 𝜓)) |
| 3 | 2 | ralimia 3080 | 1 ⊢ (∀𝑥 ∈ 𝐴 𝜑 → ∀𝑥 ∈ 𝐴 𝜓) |
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