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Mirrors > Home > ILE Home > Th. List > nfoprab2 | GIF version |
Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 25-Apr-1995.) (Revised by David Abernethy, 30-Jul-2012.) |
Ref | Expression |
---|---|
nfoprab2 | ⊢ Ⅎ𝑦{〈〈𝑥, 𝑦〉, 𝑧〉 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-oprab 5730 | . 2 ⊢ {〈〈𝑥, 𝑦〉, 𝑧〉 ∣ 𝜑} = {𝑤 ∣ ∃𝑥∃𝑦∃𝑧(𝑤 = 〈〈𝑥, 𝑦〉, 𝑧〉 ∧ 𝜑)} | |
2 | nfe1 1453 | . . . 4 ⊢ Ⅎ𝑦∃𝑦∃𝑧(𝑤 = 〈〈𝑥, 𝑦〉, 𝑧〉 ∧ 𝜑) | |
3 | 2 | nfex 1597 | . . 3 ⊢ Ⅎ𝑦∃𝑥∃𝑦∃𝑧(𝑤 = 〈〈𝑥, 𝑦〉, 𝑧〉 ∧ 𝜑) |
4 | 3 | nfab 2258 | . 2 ⊢ Ⅎ𝑦{𝑤 ∣ ∃𝑥∃𝑦∃𝑧(𝑤 = 〈〈𝑥, 𝑦〉, 𝑧〉 ∧ 𝜑)} |
5 | 1, 4 | nfcxfr 2250 | 1 ⊢ Ⅎ𝑦{〈〈𝑥, 𝑦〉, 𝑧〉 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 = wceq 1312 ∃wex 1449 {cab 2099 Ⅎwnfc 2240 〈cop 3494 {coprab 5727 |
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-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-oprab 5730 |
This theorem is referenced by: ssoprab2b 5780 nfmpo2 5791 ovi3 5859 tposoprab 6129 |
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