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Mirrors > Home > ILE Home > Th. List > nfrab1 | GIF version |
Description: The abstraction variable in a restricted class abstraction isn't free. (Contributed by NM, 19-Mar-1997.) |
Ref | Expression |
---|---|
nfrab1 | ⊢ Ⅎ𝑥{𝑥 ∈ 𝐴 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2402 | . 2 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
2 | nfab1 2260 | . 2 ⊢ Ⅎ𝑥{𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
3 | 1, 2 | nfcxfr 2255 | 1 ⊢ Ⅎ𝑥{𝑥 ∈ 𝐴 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 ∈ wcel 1465 {cab 2103 Ⅎwnfc 2245 {crab 2397 |
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-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rab 2402 |
This theorem is referenced by: repizf2 4056 rabxfrd 4360 onintrab2im 4404 tfis 4467 fvmptssdm 5473 infssuzcldc 11571 imasnopn 12395 |
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