Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rabexf | Structured version Visualization version GIF version |
Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
rabexf.1 | ⊢ Ⅎ𝑥𝐴 |
rabexf.2 | ⊢ 𝐴 ∈ 𝑉 |
Ref | Expression |
---|---|
rabexf | ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabexf.2 | . 2 ⊢ 𝐴 ∈ 𝑉 | |
2 | rabexf.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | rabexgf 41279 | . 2 ⊢ (𝐴 ∈ 𝑉 → {𝑥 ∈ 𝐴 ∣ 𝜑} ∈ V) |
4 | 1, 3 | ax-mp 5 | 1 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2110 Ⅎwnfc 2961 {crab 3142 Vcvv 3494 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-sep 5202 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-v 3496 df-in 3942 df-ss 3951 |
This theorem is referenced by: limsupequzmpt2 41997 liminfequzmpt2 42070 |
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