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Mirrors > Home > ILE Home > Th. List > riotacl2 | Unicode version |
Description: Membership law for
"the unique element in ![]() ![]() (Contributed by NM, 21-Aug-2011.) (Revised by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
riotacl2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-reu 2462 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | iotacl 5201 |
. . 3
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3 | 1, 2 | sylbi 121 |
. 2
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4 | df-riota 5830 |
. 2
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5 | df-rab 2464 |
. 2
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6 | 3, 4, 5 | 3eltr4g 2263 |
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-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-nf 1461 df-sb 1763 df-eu 2029 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-un 3133 df-sn 3598 df-pr 3599 df-uni 3810 df-iota 5178 df-riota 5830 |
This theorem is referenced by: riotacl 5844 riotasbc 5845 supubti 6997 suplubti 6998 grplinv 12876 |
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