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Mirrors > Home > MPE Home > Th. List > zfausab | Structured version Visualization version 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 3686 | . 2 ⊢ {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} ⊆ 𝐴 | |
3 | 1, 2 | ssexi 4803 | 1 ⊢ {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 384 ∈ wcel 1990 {cab 2608 Vcvv 3200 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ss 3588 |
This theorem is referenced by: rabfmpunirn 29453 |
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