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| Mirrors > Home > MPE Home > Th. List > ralrimiva | Structured version Visualization version GIF version | ||
| Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 2-Jan-2006.) |
| Ref | Expression |
|---|---|
| ralrimiva.1 | ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → 𝜓) |
| Ref | Expression |
|---|---|
| ralrimiva | ⊢ (𝜑 → ∀𝑥 ∈ 𝐴 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ralrimiva.1 | . . 3 ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → 𝜓) | |
| 2 | 1 | ex 412 | . 2 ⊢ (𝜑 → (𝑥 ∈ 𝐴 → 𝜓)) |
| 3 | 2 | ralrimiv 3145 | 1 ⊢ (𝜑 → ∀𝑥 ∈ 𝐴 𝜓) |
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