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Mirrors > Home > ILE Home > Th. List > nfriota1 | GIF version |
Description: The abstraction variable in a restricted iota descriptor isn't free. (Contributed by NM, 12-Oct-2011.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfriota1 | ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-riota 5684 | . 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfiota1 5048 | . 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 Ⅎwnfc 2242 ℩cio 5044 ℩crio 5683 |
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 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-rex 2396 df-sn 3499 df-uni 3703 df-iota 5046 df-riota 5684 |
This theorem is referenced by: riotaprop 5707 riotass2 5710 riotass 5711 lble 8612 oddpwdclemdvds 11690 oddpwdclemndvds 11691 |
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