Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > riotaund | Unicode version |
Description: Restricted iota equals the empty set when not meaningful. (Contributed by NM, 16-Jan-2012.) (Revised by Mario Carneiro, 15-Oct-2016.) (Revised by NM, 13-Sep-2018.) |
Ref | Expression |
---|---|
riotaund |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-riota 5730 | . 2 | |
2 | df-reu 2423 | . . 3 | |
3 | iotanul 5103 | . . 3 | |
4 | 2, 3 | sylnbi 667 | . 2 |
5 | 1, 4 | syl5eq 2184 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1331 wcel 1480 weu 1999 wreu 2418 c0 3363 cio 5086 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-in1 603 ax-in2 604 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-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-reu 2423 df-v 2688 df-dif 3073 df-in 3077 df-ss 3084 df-nul 3364 df-sn 3533 df-uni 3737 df-iota 5088 df-riota 5730 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |