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| Mirrors > Home > MPE Home > Th. List > ssrab2 | Structured version Visualization version GIF version | ||
| Description: Subclass relation for a restricted class. (Contributed by NM, 19-Mar-1997.) (Proof shortened by BJ and SN, 8-Aug-2024.) |
| Ref | Expression |
|---|---|
| ssrab2 | ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ⊆ 𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elrabi 3687 | . 2 ⊢ (𝑦 ∈ {𝑥 ∈ 𝐴 ∣ 𝜑} → 𝑦 ∈ 𝐴) | |
| 2 | 1 | ssriv 3987 | 1 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ⊆ 𝐴 |
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