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Mirrors > Home > MPE Home > Th. List > ralrimi | Structured version Visualization version GIF version |
Description: Inference from Theorem 19.21 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 10-Oct-1999.) Shortened after introduction of hbralrimi 3103. (Revised by Wolf Lammen, 4-Dec-2019.) |
Ref | Expression |
---|---|
ralrimi.1 | ⊢ Ⅎ𝑥𝜑 |
ralrimi.2 | ⊢ (𝜑 → (𝑥 ∈ 𝐴 → 𝜓)) |
Ref | Expression |
---|---|
ralrimi | ⊢ (𝜑 → ∀𝑥 ∈ 𝐴 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralrimi.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | nf5ri 2193 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | ralrimi.2 | . 2 ⊢ (𝜑 → (𝑥 ∈ 𝐴 → 𝜓)) | |
4 | 2, 3 | hbralrimi 3103 | 1 ⊢ (𝜑 → ∀𝑥 ∈ 𝐴 𝜓) |
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