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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 2423 | . 2 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
2 | nfab1 2281 | . 2 ⊢ Ⅎ𝑥{𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
3 | 1, 2 | nfcxfr 2276 | 1 ⊢ Ⅎ𝑥{𝑥 ∈ 𝐴 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 ∈ wcel 1480 {cab 2123 Ⅎwnfc 2266 {crab 2418 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rab 2423 |
This theorem is referenced by: repizf2 4081 rabxfrd 4385 onintrab2im 4429 tfis 4492 fvmptssdm 5498 infssuzcldc 11633 imasnopn 12457 |
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