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Mirrors > Home > ILE Home > Th. List > zfausab | GIF version |
Description: Separation Scheme (Aussonderung) in terms of a class abstraction. (Contributed by NM, 8-Jun-1994.) |
Ref | Expression |
---|---|
zfausab.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
zfausab | ⊢ {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfausab.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | ssab2 3186 | . 2 ⊢ {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} ⊆ 𝐴 | |
3 | 1, 2 | ssexi 4074 | 1 ⊢ {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} ∈ V |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 ∈ wcel 1481 {cab 2126 Vcvv 2689 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-in 3082 df-ss 3089 |
This theorem is referenced by: (None) |
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