| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > rabex | Structured version Visualization version GIF version | ||
| Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by NM, 19-Jul-1996.) |
| Ref | Expression |
|---|---|
| rabex.1 | ⊢ 𝐴 ∈ V |
| Ref | Expression |
|---|---|
| rabex | ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rabex.1 | . 2 ⊢ 𝐴 ∈ V | |
| 2 | rabexg 5337 | . 2 ⊢ (𝐴 ∈ V → {𝑥 ∈ 𝐴 ∣ 𝜑} ∈ V) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ∈ V |
| Copyright terms: Public domain | W3C validator |