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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 2399 | . 2 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
2 | nfab1 2257 | . 2 ⊢ Ⅎ𝑥{𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
3 | 1, 2 | nfcxfr 2252 | 1 ⊢ Ⅎ𝑥{𝑥 ∈ 𝐴 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 ∈ wcel 1463 {cab 2101 Ⅎwnfc 2242 {crab 2394 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-11 1467 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-rab 2399 |
This theorem is referenced by: repizf2 4046 rabxfrd 4350 onintrab2im 4394 tfis 4457 fvmptssdm 5459 infssuzcldc 11492 imasnopn 12310 |
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