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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-riota 5833 |
. 2
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2 | df-reu 2462 |
. . 3
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3 | iotanul 5195 |
. . 3
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4 | 2, 3 | sylnbi 678 |
. 2
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5 | 1, 4 | eqtrid 2222 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-reu 2462 df-v 2741 df-dif 3133 df-in 3137 df-ss 3144 df-nul 3425 df-sn 3600 df-uni 3812 df-iota 5180 df-riota 5833 |
This theorem is referenced by: (None) |
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