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| Mirrors > Home > MPE Home > Th. List > rexlimdva | Structured version Visualization version GIF version | ||
| Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 20-Jan-2007.) |
| Ref | Expression |
|---|---|
| rexlimdva.1 | ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| rexlimdva | ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rexlimdva.1 | . . 3 ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → (𝜓 → 𝜒)) | |
| 2 | 1 | ex 412 | . 2 ⊢ (𝜑 → (𝑥 ∈ 𝐴 → (𝜓 → 𝜒))) |
| 3 | 2 | rexlimdv 3153 | 1 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
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