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| Mirrors > Home > MPE Home > Th. List > reximdv | Structured version Visualization version GIF version | ||
| Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version with strong hypothesis.) (Contributed by NM, 24-Jun-1998.) |
| Ref | Expression |
|---|---|
| ralimdv.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| reximdv | ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → ∃𝑥 ∈ 𝐴 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ralimdv.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 2 | 1 | a1d 25 | . 2 ⊢ (𝜑 → (𝑥 ∈ 𝐴 → (𝜓 → 𝜒))) |
| 3 | 2 | reximdvai 3165 | 1 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → ∃𝑥 ∈ 𝐴 𝜒)) |
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