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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 2309 | . 2 ⊢ {x ∈ A ∣ φ} = {x ∣ (x ∈ A ∧ φ)} | |
2 | nfab1 2177 | . 2 ⊢ Ⅎx{x ∣ (x ∈ A ∧ φ)} | |
3 | 1, 2 | nfcxfr 2172 | 1 ⊢ Ⅎx{x ∈ A ∣ φ} |
Colors of variables: wff set class |
Syntax hints: ∧ wa 97 ∈ wcel 1390 {cab 2023 Ⅎwnfc 2162 {crab 2304 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rab 2309 |
This theorem is referenced by: repizf2 3906 rabxfrd 4167 tfis 4249 fvmptssdm 5198 |
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