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| Mirrors > Home > MPE Home > Th. List > resex | Structured version Visualization version GIF version | ||
| Description: The restriction of a set is a set. (Contributed by Jeff Madsen, 19-Jun-2011.) |
| Ref | Expression |
|---|---|
| resex.1 | ⊢ 𝐴 ∈ V |
| Ref | Expression |
|---|---|
| resex | ⊢ (𝐴 ↾ 𝐵) ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | resex.1 | . 2 ⊢ 𝐴 ∈ V | |
| 2 | resexg 6045 | . 2 ⊢ (𝐴 ∈ V → (𝐴 ↾ 𝐵) ∈ V) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 ↾ 𝐵) ∈ V |
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