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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 44171 | . 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 2105 Ⅎwnfc 2882 {crab 3431 Vcvv 3473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-sep 5299 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1543 df-ex 1781 df-nf 1785 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-rab 3432 df-v 3475 df-in 3955 df-ss 3965 |
This theorem is referenced by: limsupequzmpt2 44893 liminfequzmpt2 44966 fsupdm 46017 finfdm 46021 |
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