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 42181 | . 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 2112 Ⅎwnfc 2877 {crab 3055 Vcvv 3398 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2018 ax-8 2114 ax-9 2122 ax-10 2143 ax-11 2160 ax-12 2177 ax-ext 2708 ax-sep 5177 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-ex 1788 df-nf 1792 df-sb 2073 df-clab 2715 df-cleq 2728 df-clel 2809 df-nfc 2879 df-rab 3060 df-v 3400 df-in 3860 df-ss 3870 |
This theorem is referenced by: limsupequzmpt2 42877 liminfequzmpt2 42950 |
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