![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 2477 | . 2 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
2 | nfab1 2334 | . 2 ⊢ Ⅎ𝑥{𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
3 | 1, 2 | nfcxfr 2329 | 1 ⊢ Ⅎ𝑥{𝑥 ∈ 𝐴 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: ∧ wa 104 ∈ wcel 2160 {cab 2175 Ⅎwnfc 2319 {crab 2472 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rab 2477 |
This theorem is referenced by: repizf2 4180 rabxfrd 4487 onintrab2im 4535 tfis 4600 fvmptssdm 5621 infssuzcldc 11987 nnwosdc 12075 imasnopn 14276 |
Copyright terms: Public domain | W3C validator |