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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 2323 | . 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 5826 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wnf 1453 wcel 2141 wnfc 2299 wreu 2450 crio 5805 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-reu 2455 df-v 2732 df-sbc 2956 df-un 3125 df-sn 3587 df-pr 3588 df-uni 3795 df-iota 5158 df-riota 5806 |
This theorem is referenced by: riota2 5828 riotaprop 5829 riotass2 5832 riotass 5833 |
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