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Mirrors > Home > ILE Home > Th. List > riota2f | Unicode version |
Description: This theorem shows a condition that allows us to represent a descriptor with a class expression . (Contributed by NM, 23-Aug-2011.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
riota2f.1 | |
riota2f.2 | |
riota2f.3 |
Ref | Expression |
---|---|
riota2f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | riota2f.1 | . . 3 | |
2 | 1 | nfel1 2292 | . 2 |
3 | 1 | a1i 9 | . 2 |
4 | riota2f.2 | . . 3 | |
5 | 4 | a1i 9 | . 2 |
6 | id 19 | . 2 | |
7 | riota2f.3 | . . 3 | |
8 | 7 | adantl 275 | . 2 |
9 | 2, 3, 5, 6, 8 | riota2df 5750 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wnf 1436 wcel 1480 wnfc 2268 wreu 2418 crio 5729 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-reu 2423 df-v 2688 df-sbc 2910 df-un 3075 df-sn 3533 df-pr 3534 df-uni 3737 df-iota 5088 df-riota 5730 |
This theorem is referenced by: riota2 5752 riotaprop 5753 riotass2 5756 riotass 5757 |
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